A fair coin is flipped 6 times. What is the probability of exactly 3 heads?

A fair coin is flipped 6 times. What is the probability of exactly 3 heads?

• A. 3/8
• B. 5/16
• C. 1/2
• D. 3/16

Answer: (B)

Think of this as a binomial probability: the number of heads in six independent fair coin flips follows a binomial distribution. To get exactly three heads, first count how many sequences have three heads and three tails. There are C(6,3) ways to choose which flips show heads, and that equals 20. Each specific sequence has probability (1/2)^6 = 1/64 because each flip is independent and has probability 1/2. Multiply the number of sequences by the probability of each sequence: 20 × 1/64 = 20/64 = 5/16. So the probability is 5/16.

Think of this as a binomial probability: the number of heads in six independent fair coin flips follows a binomial distribution. To get exactly three heads, first count how many sequences have three heads and three tails. There are C(6,3) ways to choose which flips show heads, and that equals 20. Each specific sequence has probability (1/2)^6 = 1/64 because each flip is independent and has probability 1/2. Multiply the number of sequences by the probability of each sequence: 20 × 1/64 = 20/64 = 5/16. So the probability is 5/16.