Question

37. In a class of 20 students each student tosses a fair coin 4 times independently.

(a) What is the probability that no student gets 4 heads?

(b) What is the expected number of students who get 4 heads?

Answer 1

Here' the answer to the question. Write back in case you've not understood any part of it. Have a great week!

Lets X be even to getting 4 heads out of 4 tosses. This happens with a probability of 1/2^4 = 1/16

a.

P( no student gets 4 heads) = ?

We use the binomial distribution to model event X. X is the event as defined above.

n = 20, p = 1/16 = .0625

P(no students gets 4 heads) = P(X,n,p) = P(0, 20, .0625)

= 20C0 * .625^0 * .375^20

= 0.2751

Answer is 0.2751

b.

Expected number of students to get 4 heads = n*p

= 20 * .0625

= 1.25

Answer is 1.25