Question

A fair die is thrown three times. What is the probability of getting exactly two 6s?

• A. \(\frac{5}{72}\)
• B. \(\frac{1}{18}\)
• C. \(\frac{1}{12}\)
• D. \(\frac{7}{72}\)

Hint:

Think about how many ways you can pick which single throw is the "non-six" among the three throws, then count outcomes for each face.

Answer 1

The Correct Option is A

Exactly two 6s means two throws show 6 and one throw shows a non-6. Probability \(= \binom{3}{2}\left(\frac{1}{6}\right)^2\left(\frac{5}{6}\right) = 3\cdot\frac{1}{36}\cdot\frac{5}{6}=\frac{15}{216}=\frac{5}{72}\). Correct option: \(\frac{5}{72}\).