Probability
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Q.

One hundred identical coins each with probability '$p$' showing up heads and tossed

If $0<p<1$ and the probability of heads showing on 50 coins is equal to that of heads on 51 coins, then the value of $p$ is:

 A.

1/2

 B.

49/101

 C.

50/101

 D.

51/101

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Solution:
Option(D) is correct

Let $a$ be the number of coins showing heads

Then, $P(A=50)=P(A=51)$

\(\begin{align*} \Rightarrow ^{100}C_{50}\times P^{50}\times (1-P)^{50}\\ \Rightarrow ^{100}C_{51}\times P^{51}\times (1-P)^{49}\\ \Rightarrow ^{100}C_{50}\times P^{51}\times (1-P)^{50}=^{100}C_{51}\times P\\ \Rightarrow 51(1−P)=50P\\ \Rightarrow P = 51/101 \end{align*}\)


(10) Comment(s)


Aritra Das
 ()

Why $^{100}C_{50}$ and$^{100}C_{51}$ and .... ? The coins are identical, meaning thereby that the only distinction between them is head or tails. As a result, it does not matter which 50 or 51 turn heads up.



Sushma Saroj
 ()

yes that type of difficult questions shouldn't be asked in any kind of exams.

That type of questions is really tough


Sangeetha Mani
 ()

I guess this question can be solved easily by using poisson distributiion


Shivanand
 ()

Out of a hundred 'identical' coins, selecting one set of 50 coins is not different from selecting another set of 50 coins since they are all identical.

The answer should be 1/2



Parul
 ()

No all u r are wrong. 

These questions will make student think..

They would come to know their skills...



Sagar
 ()

such questions makes students depressed and this the reason for unemployability...so its my humble, kind and genuine request not to post such questions to avoid any damage to students...



Hiren
 ()

Such questions make students frustrated and that is the reason of students attempting suicide.

So, please don't post such tough questions?...


Parul
 ()

And please Hiren can you tell me how due to dis ques can a person will attempt suicide...???Mad


Ankit
 ()

Please don't ask such questions.

Students get demotivated.Sad


HimiK
 ()

I agree.

This gave me a headache.