Multiple choice

A fair die is rolled repeatedly until a six is obtained. Let X denote the number of rolls required. The probability that $P(X\leq 2)$ equals

  1. $\displaystyle \frac{125}{216}$
  2. $\displaystyle \frac{11}{36}$
  3. $\displaystyle \frac{5}{36}$
  4. $\displaystyle \frac{25}{216}$
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B Correct answer
Explanation

P(X <= 2) = P(X=1) + P(X=2). P(X=1) = 1/6. P(X=2) = (5/6) * (1/6) = 5/36. Sum = 6/36 + 5/36 = 11/36.

AI explanation

Using the probability formula, the chance of getting a six in a single roll is 1/6. The probability of getting a six on the first roll is 1/6, and the probability of not getting a six on the first roll but getting one on the second roll is (5/6) times (1/6), which equals 5/36. Adding these two probabilities together gives 1/6 + 5/36 = 6/36 + 5/36 = 11/36.

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