If a fair coin is flipped 30 times a What is the probability

If a fair coin is flipped 30 times: a. What is the probability that exactly 15 of the outcomes will be heads? b. What is the probability that either 15 or 16 of the outcomes will be heads? Please do step by step. Thx

Solution

fair coin so P(head) = 0.5 P(tail) = 0.5 n = 30

a)

binomial distribution

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

nCx = combination

P(x=15) = 30C15 * 0.5^15 * 0.5^(30-15) = 0.14446

b)

What is the probability that either 15 or 16 of the outcomes will be heads?

P(x=15) + P(X=16)

P(x=16)= 30C16 * 0.5^16 * 0.5^(30-16) = 0.1354

P(x=15) + P(X=16)= 0.1354 + 0.14446 = 0.2799