Multiple choice

A fair die is rolled repeatedly until a six is obtained. Let X denote the number of rolls required. The conditional probability that $X \geq 6$ given $X > 3$ equals

  1. $\displaystyle \frac{125}{216}$
  2. $\displaystyle \frac{25}{216}$
  3. $\displaystyle \frac{5}{36}$
  4. $\displaystyle \frac{25}{36}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is a geometric distribution. P(X >= 6 | X > 3) = P(X >= 6) / P(X > 3). P(X > 3) = (5/6)^3. P(X >= 6) = (5/6)^5. Ratio = (5/6)^5 / (5/6)^3 = (5/6)^2 = 25/36.

Keep practicing — related questions