Question

A fair coin is flipped 9 times, and the sequence of heads and tails is recorded. Find the probabilitythat there are exactly 4 heads in the sequence. Enter your answer as a decimal number rounded toFOUR digits after the decimal point.

Answer 1

Answer: 0.2461.

Explanation:

You can model this exactly as a binomial distribution. Since the coin is fair, then the probability of flipping a head = 0.5. Let X ~ Bin(9, 0.5) model the number of heads after flipping the coin 9 times. You want to, therefore, compute

P(X = 4) = C(9, 4) * 0.5^4 * 0.5^5
= C(9, 4) * 0.5^9
= 0.2461 (rounded to four decimal places).