Question

A fair coin is flipped six times. Find the probability that heads comes up exactly four times.

1/16

15/64

90/16

1/4

2/3

Answer 1

solution:

Let X be the discrete random variable representing the No.of heads

Given that

No.of trials (n) = 6

Probability of Head (p) = 1/2 [ since given that it is a fair coin ]

Probability of Tail (1-p) = 1/2

Here, X ~B(n,p)

~B(6 , 1/2)

we know that

P(X=x) = nCx * (p)^x * (1-p)^(n-x)

Probability that Head comes exactly 4 times = P(X=4)

  = 6C4 * (1/2)^4 * (1/2)^2

= 15 * (1/2)^6

= 15 / (2)^6

= 15 / 64

   Probability that Head comes exactly 4 times = 15 / 64

So,Option-B is correct