You toss a fair coin four times: A: what is the probability of that you observe

Question

You toss a fair coin four times:

A: what is the probability of that you observe exactly two heads? B: what is the probability of at least three heads?

C: given that you have observed at least one heads, what is the probability that you observe at least two heads?

Q1: 20 Points You toss a fair coin four times: A: what is the probability of that you observe exactly two heads? B: what is the probability of at least three heads? C: given that you have observed at least one heads, what is the probability that you observe at least two heads?

Explanation / Answer

Part-A

Let X be the number of heads in 4 throws then X follows Binomial distribution with n=4 and p=0.5.

So, P(X=2)=0.375 using excel =BINOMDIST(2,4,0.5,FALSE)

Part-B

P(X>=3)=0.3125 using excel =1-BINOMDIST(2,4,0.5,TRUE)

Part-C

P(X>=2/X>=1)= P(X>=2)/P(X>=1) = 0.73 using following excel

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