According to a prominent investment adviser, Company X has a 50% chanc : Two-part Analysis (TPA)

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chienp054

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

07 Dec 2023, 02:55

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OFFICIAL EXPLANATION

Infer
RO1, Least probability for both:
To determine what the least probability is of both Company X and Company Y posting a profit in the coming year, determine what is the greatest probability of one of the companies—say Company X—posting a profit and the other company—Company Y—not posting a profit, and then subtract that result from the probability of Company X posting a profit. Because the probability of Company Y posting a profit in the coming year is 60%, then the probability of Company Y not posting a profit in the coming year is 40%. The greatest probability of Company X posting a profit and Company Y not posting a profit in the coming year cannot exceed the lesser of the probability of Company X posting a profit in the coming year—which is 50%—and the probability of Company Y not posting a profit in the coming year—which is 40%. Therefore, at most, the probability of both Company X posting a profit but Company Y not posting a profit in the coming year is 40%. Subtracting the 40% probability of Company X posting a profit from the probability of Company Y not posting a profit from the 50% probability of Company X posting a profit gives us the least probability of both Company X and Company Y posting a profit in the coming year, namely 10%.

The correct answer is 10%.

RO2, Greatest probability for both:
The greatest probability of both Company X and Company Y posting a profit in the coming year cannot exceed the lesser of the probability of Company X posting a profit in the coming year—which is 50%—and the probability of Company Y posting a profit in the coming year—which is 60%. Therefore, the greatest probability of both Company X and Company Y posting a profit in the coming year is 50%.

The correct answer is 50%.

This is the official answer. I'm trying to wrap my head around it as well. So if anyone can care to dumb it down for me. That will be appreciated!

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

08 Dec 2023, 09:09

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IS THIS DATA INSIGHTS?

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AvikSaha

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

04 Jan 2024, 05:39

MartyMurray Can you please help here to explain the approach to solve this

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kittle

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

27 Mar 2024, 08:18

MartyMurray - would you recommend skipping this question in exam? I was not able to wrap my head around how to solve this.

MartyMurray wrote:

AvikSaha wrote:

MartyMurray Can you please help here to explain the approach to solve this

According to a prominent investment adviser, Company X has a 50% chance of posting a profit in the coming year, whereas Company Y has 60% chance of posting a profit in the coming year.

Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.

An intuitive way to handle this question is to see the following.

The maximum probability of any event occurring is 1. So, the maximum probability that either X will post a profit or Y will post a profit is 1.

Now, since 50% + 60% > 1, we see that there must be some times when both occur. In other words, the occurrences of the two events must overlap some of the time. After all, if they didn't overlap, the probability that one or the other would occur would be greater than 1.

If you think about it, the minimum overlap must be 10%. After all, if we fill up 50% of the possible total probability of 1 with the probability that X will be profitable, then we have only 50% of the possible total probability of 1 left for Y. However, the probability that Y will be profitable is 60%. So, that 60% - 50% = 10% extra must overlap with the occurrence of X being profitable.

In mathematical terms, P(X or Y) = P(X) + P(Y) - P(X and Y), and it must be the case that P(X or Y) ≤ 1.

So, if P(X) + P(Y) = 0.5 + 0.6 = 1.1, then to reduce 1.1 to the maximum P(X or Y) of 1, we need to subtract at least 0.1.

Thus, P(X and Y) must be at least 0.1, meaning the correct answer for Least Probability for Both is 10%.

Then, the maximum probability that both will occur at the same time must be 50% since the maximum probability of X posting a profit is 50% and the probability of both posting a profit can't be greater than the probability that one of them will.

So, the correct answer for Greatest Probability for Both is 50%.

Correct Answer: 10%, 50%

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MartyMurray

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According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

28 Mar 2024, 10:35

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Expert Reply

kittle wrote:

MartyMurray - would you recommend skipping this question in exam? I was not able to wrap my head around how to solve this.

I'd recommend learning how to answer this question, which isn't very complex actually, because there are at least two questions that work like this one on the Focus Edition practice tests. So, it appears that GMAC's question-writers may be into involving this concept in questions.

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Gmatguy007

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

31 Mar 2024, 09:32

MartyMurray wrote:

AvikSaha wrote:

MartyMurray Can you please help here to explain the approach to solve this

According to a prominent investment adviser, Company X has a 50% chance of posting a profit in the coming year, whereas Company Y has 60% chance of posting a profit in the coming year.

Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.

An intuitive way to handle this question is to see the following.

The maximum probability of any event occurring is 1. So, the maximum probability that either X will post a profit or Y will post a profit is 1.

Now, since 50% + 60% > 1, we see that there must be some times when both occur. In other words, the occurrences of the two events must overlap some of the time. After all, if they didn't overlap, the probability that one or the other would occur would be greater than 1.

If you think about it, the minimum overlap must be 10%. After all, if we fill up 50% of the possible total probability of 1 with the probability that X will be profitable, then we have only 50% of the possible total probability of 1 left for Y. However, the probability that Y will be profitable is 60%. So, that 60% - 50% = 10% extra must overlap with the occurrence of X being profitable.

In mathematical terms, P(X or Y) = P(X) + P(Y) - P(X and Y), and it must be the case that P(X or Y) ≤ 1.

So, if P(X) + P(Y) = 0.5 + 0.6 = 1.1, then to reduce 1.1 to the maximum P(X or Y) of 1, we need to subtract at least 0.1.

Thus, P(X and Y) must be at least 0.1, meaning the correct answer for Least Probability for Both is 10%.

Then, the maximum probability that both will occur at the same time must be 50% since the maximum probability of X posting a profit is 50% and the probability of both posting a profit can't be greater than the probability that one of them will.

So, the correct answer for Greatest Probability for Both is 50%.

Correct Answer: 10%, 50%

I chose these two but for the least probability I was between 5% and 10%. I thought that it would be the difference between the probability for X and Y. Is it a coincidence or it can be explained somehow?

Thank you in advance MartyMurray

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cookiemonsterpsy

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

10 Apr 2024, 05:35

mike12543 wrote:

i am not sure whether i know math after seeing this question.

me too

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cookiemonsterpsy

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

10 Apr 2024, 05:43

Gmatguy007 wrote:

MartyMurray wrote:

AvikSaha wrote:

MartyMurray Can you please help here to explain the approach to solve this

According to a prominent investment adviser, Company X has a 50% chance of posting a profit in the coming year, whereas Company Y has 60% chance of posting a profit in the coming year.

Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.

An intuitive way to handle this question is to see the following.

The maximum probability of any event occurring is 1. So, the maximum probability that either X will post a profit or Y will post a profit is 1.

Now, since 50% + 60% > 1, we see that there must be some times when both occur. In other words, the occurrences of the two events must overlap some of the time. After all, if they didn't overlap, the probability that one or the other would occur would be greater than 1.

If you think about it, the minimum overlap must be 10%. After all, if we fill up 50% of the possible total probability of 1 with the probability that X will be profitable, then we have only 50% of the possible total probability of 1 left for Y. However, the probability that Y will be profitable is 60%. So, that 60% - 50% = 10% extra must overlap with the occurrence of X being profitable.

In mathematical terms, P(X or Y) = P(X) + P(Y) - P(X and Y), and it must be the case that P(X or Y) ≤ 1.

So, if P(X) + P(Y) = 0.5 + 0.6 = 1.1, then to reduce 1.1 to the maximum P(X or Y) of 1, we need to subtract at least 0.1.

Thus, P(X and Y) must be at least 0.1, meaning the correct answer for Least Probability for Both is 10%.

Then, the maximum probability that both will occur at the same time must be 50% since the maximum probability of X posting a profit is 50% and the probability of both posting a profit can't be greater than the probability that one of them will.

So, the correct answer for Greatest Probability for Both is 50%.

Correct Answer: 10%, 50%

I chose these two but for the least probability I was between 5% and 10%. I thought that it would be the difference between the probability for X and Y. Is it a coincidence or it can be explained somehow?

Thank you in advance MartyMurray

i am curious too. if the prob was 50% and 40%, would the ans for RO1 be 0? since there is no "overlap"?

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Gmatguy007

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According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

Updated on: 17 Apr 2024, 06:50

cookiemonsterpsy wrote:

i am curious too. if the prob was 50% and 40%, would the ans for RO1 be 0? since there is no "overlap"?

My way of thinking was to draw a bar chart and I saw that for both having a profit, the maximum chance would be 40% (which is the greatest common level) and for the minimum the one with the greatest chance (the 50%) would have to sacrifice 10%.

So I think it would be 10% and 40% but GMATCoachBen KarishmaB manasp35 I would really like your opinion on this to make this kind of question crystal clear

Originally posted by Gmatguy007 on 10 Apr 2024, 12:12.
Last edited by Gmatguy007 on 17 Apr 2024, 06:50, edited 3 times in total.

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tribui

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According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

11 Apr 2024, 22:00

Quote:

MartyMurray

AvikSaha wrote:

MartyMurray Can you please help here to explain the approach to solve this

According to a prominent investment adviser, Company X has a 50% chance of posting a profit in the coming year, whereas Company Y has 60% chance of posting a profit in the coming year.

Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.

An intuitive way to handle this question is to see the following.

The maximum probability of any event occurring is 1. So, the maximum probability that either X will post a profit or Y will post a profit is 1.

Now, since 50% + 60% > 1, we see that there must be some times when both occur. In other words, the occurrences of the two events must overlap some of the time. After all, if they didn't overlap, the probability that one or the other would occur would be greater than 1.

If you think about it, the minimum overlap must be 10%. After all, if we fill up 50% of the possible total probability of 1 with the probability that X will be profitable, then we have only 50% of the possible total probability of 1 left for Y. However, the probability that Y will be profitable is 60%. So, that 60% - 50% = 10% extra must overlap with the occurrence of X being profitable.

In mathematical terms, P(X or Y) = P(X) + P(Y) - P(X and Y), and it must be the case that P(X or Y) ≤ 1.

So, if P(X) + P(Y) = 0.5 + 0.6 = 1.1, then to reduce 1.1 to the maximum P(X or Y) of 1, we need to subtract at least 0.1.

Thus, P(X and Y) must be at least 0.1, meaning the correct answer for Least Probability for Both is 10%.

Then, the maximum probability that both will occur at the same time must be 50% since the maximum probability of X posting a profit is 50% and the probability of both posting a profit can't be greater than the probability that one of them will.

So, the correct answer for Greatest Probability for Both is 50%.

Correct Answer: 10%, 50%

Marty Murray thks for the answer, an equivalence of what you just decribed is basically a Venn diagram with 100% total probability. Then P(X) and P(Y) have to fit inside this total anywhere and you can clearly see that by moving the area representing P(X) and P(Y) around the greatest overlap is 50% and the least overlap is 10% (and, they have to overlap since their sum is greater than 110%)

BUT I have a huge problem with the quality of this question. In fact, even with getting the correct numerical answer, I cannot tolerate this question because it is obviously faulty in relation to any kind of basic probability framework. The way question is set up, you dont even know if the probabilities are independent or not? (the answer to which would totally change the answer). Also, the biggest blunder is again, with the setup and wording, this is definitely NOT a categorical logic set up (where you explanation above or the Venn diagram could be used). These are 2 EVENTS and they could be independent (or dependent) and then you could just multiple the probabilities or you have to use a probability trees ...

If someone can point out the correct logic for me, I'd appreciate it, but I get angry (at the GMAC) looking at this question. In fact, anyone know if and how can we report a bad question to the GMAC? This question is not acceptable.

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

17 Apr 2024, 08:00

Gmatguy007 wrote:

cookiemonsterpsy wrote:

i am curious too. if the prob was 50% and 40%, would the ans for RO1 be 0? since there is no "overlap"?

My way of thinking was to draw a bar chart and I saw that for both having a profit, the maximum chance would be 40% (which is the greatest common level) and for the minimum the one with the greatest chance (the 50%) would have to sacrifice 10%.

Different Approach (for understanding purpose)

Let
x = only X is profitable
y = only Y is profitable
b = both profitable
a = none are profitable

Given
x + b = 50 meaning b = 50 - x , according to this
b max is 50, b min is 0 --- eq 1
y + b = 40 meaning b = 40 - y , according to this
b max is 40, b min is 0 -- eq 2

Adding above equations, x + y + 2b = 90

x + y + a + b = 100
but x + y = 90 -2b

90 - 2b + a + b = 100
b = a - 10 , according to this
b max is 90, b min is 0 ---- eq 3

combining eq 1, eq 2, eq 3. Since b needs to satisfy all three equations
b max is 40 , b min is 0.

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Gmatguy007

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

17 Apr 2024, 08:07

manasp35 wrote:

Different Approach (for understanding purpose)

Let
x = only X is profitable
y = only Y is profitable
b = both profitable
a = none are profitable

Given
x + b = 50 meaning b = 50 - x , according to this
b max is 50, b min is 0 --- eq 1
y + b = 40 meaning b = 40 - y , according to this
b max is 40, b min is 0 -- eq 2

Adding above equations, x + y + 2b = 90

x + y + a + b = 100
but x + y = 90 -2b

90 - 2b + a + b = 100
b = a - 10 , according to this
b max is 90, b min is 0 ---- eq 3

combining eq 1, eq 2, eq 3. Since b needs to satisfy all three equations
b max is 40 , b min is 0.

So, the maximum is the minimum of the 2 given quantities (the 50,40 in particular) and minimum is zero regardless what's the difference between these two (in our example, 50-40=10), in order to both be positive.

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

17 Apr 2024, 23:32

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vsgamtttttt wrote:

According to a prominent investment adviser, Company X has a 50% chance of posting a profit in the coming year, whereas Company Y has 60% chance of posting a profit in the coming year.

Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.

The rules of probability are similar to those of Sets.

P(X) = 50%
P(Y) = 60%

P(X or Y) = P(X) + P(Y) - Both
Both = P(X) + P(Y) - P(X or Y)

If we want to minimize Both, we must maximize P(X or Y) - subtract the biggest number possible. P(X or Y) can take a maximum value of 1 because probability cannot be more than 1.

Least Probability of Both = .5 + .6 - 1 = 0.1

We can maximize 'Both' by simply putting the P(X) circle inside the P(Y) circle and hence Both = 0.5

ANSWER: Least = 10%, Greatest = 50%

Here is a video that explains how max-min is done in Sets:
https://youtu.be/oLKbIyb1ZrI

You can check how to apply the same concepts on Probability in my content on Sunday (through Super Sundays). Details here:
https://youtu.be/gN_vlDpUflo

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

17 May 2024, 22:40

Can anyone please explain why the probability of two events occuring is not simply 0.5*0.6 = 0.3

Are we to think they are dependent events? I am confused here

Posted from my mobile device

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manasp35

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Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

17 May 2024, 23:07

T4Star wrote:

Can anyone please explain why the probability of two events occuring is not simply 0.5*0.6 = 0.3

Are we to think they are dependent events? I am confused here

Posted from my mobile device

Yes you are right. We can't say they are independent, so we can't directly multiply both probabilities. Thinking from real world scenario two companies might compete with each other. Success of one can affect the success chances of other company.

Interesting question.

gmatclubot

Re: According to a prominent investment adviser, Company X has a 50% chanc [#permalink]

17 May 2024, 23:07

According to a prominent investment adviser, Company X has a 50% chanc

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