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The probability of each of 10 identical coins showing a Heads is p
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02 Jun 2019, 11:31
02 Jun 2019, 11:31
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The probability of each of 10 identical coins showing a Heads is p, where 0 < p < 1. These 10 coins are tossed once. If the probability of 5 coins showing a Heads is the same as the probability of 4 coins showing a Tails, what is the value of p?
A. 2/5
B. 5/11
C. 1/2
D. 6/11
E. 3/5
A. 2/5
B. 5/11
C. 1/2
D. 6/11
E. 3/5
Re: The probability of each of 10 identical coins showing a Heads is p
[#permalink]
03 Jun 2019, 16:39
03 Jun 2019, 16:39
1
Kudos
Probability of getting a Head=p
Probability of getting a Tail= 1-p
The probability of 5 coins showing a Heads= \(10C5*p^5*(1-p)^5\)
The probability of 4 coins showing a Tails= \(10C6*p^6*(1-p)^4\)
\(10C5*p^5*(1-p)^5\)= \(10C6*p^6*(1-p)^4\)
\(\frac{10!}{5!5!}*(1-p)\)=\(\frac{10!}{6!4!}*p\)
6-6p=5p
11p=6
p=6/11
Probability of getting a Tail= 1-p
The probability of 5 coins showing a Heads= \(10C5*p^5*(1-p)^5\)
The probability of 4 coins showing a Tails= \(10C6*p^6*(1-p)^4\)
\(10C5*p^5*(1-p)^5\)= \(10C6*p^6*(1-p)^4\)
\(\frac{10!}{5!5!}*(1-p)\)=\(\frac{10!}{6!4!}*p\)
6-6p=5p
11p=6
p=6/11
nick1816 wrote:
The probability of each of 10 identical coins showing a Heads is p, where 0 < p < 1. These 10 coins are tossed once. If the probability of 5 coins showing a Heads is the same as the probability of 4 coins showing a Tails, what is the value of p?
A. 2/5
B. 5/11
C. 1/2
D. 6/11
E. 3/5
A. 2/5
B. 5/11
C. 1/2
D. 6/11
E. 3/5
Re: The probability of each of 10 identical coins showing a Heads is p
[#permalink]
03 May 2024, 04:11
03 May 2024, 04:11
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