Three fair coins are tossed. What is the probability of getting exactly two heads?

Three fair coins are tossed. What is the probability of getting exactly two heads?

• A. 1/4
• B. 1/2
• C. 3/4
• D. 3/8

Answer: (D)

When three coins are tossed, each coin has two possible results and all eight outcomes are equally likely. To get exactly two heads, you need two of the three coins to show heads and the remaining one to show tails. There are three different ways to choose which two coins are heads. Each specific arrangement happens with probability one over eight, since all three coins must land as specified. Multiply the three favorable arrangements by their probability: three times one over eight equals three over eight. So the chance of exactly two heads is three eighths.

When three coins are tossed, each coin has two possible results and all eight outcomes are equally likely. To get exactly two heads, you need two of the three coins to show heads and the remaining one to show tails. There are three different ways to choose which two coins are heads. Each specific arrangement happens with probability one over eight, since all three coins must land as specified. Multiply the three favorable arrangements by their probability: three times one over eight equals three over eight. So the chance of exactly two heads is three eighths.