Multiple choice

A pair of fair 6-sided dice is rolled n times. What is the least value of n such that the probability that the sum of the numbers face up on a roll equals 7 at least once is greater than 1/2?

  1. 2

  2. 3

  3. 4

  4. 5

  5. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Probability of sum 7 in one roll is 6/36 = 1/6. Probability of not getting 7 in n rolls is (5/6)^n. We want 1 - (5/6)^n > 1/2, so (5/6)^n < 1/2. For n=3, (5/6)^3 = 125/216 approx 0.578. For n=4, (5/6)^4 = 625/1296 approx 0.482. Thus n=4 is the least value.

AI explanation

When two fair 6-sided dice are rolled, there are 6 outcomes where the sum is 7, giving a probability of 6/36 or 1/6. The probability of not rolling a 7 on a single roll is 5/6. We want the probability of at least one 7 in n rolls to be greater than 1/2, so we solve the inequality 1 - (5/6)^n > 1/2. Testing n = 4 gives 1 - (5/6)^4 = 1 - 625/1296 = 671/1296, which is greater than 1/2 (648/1296), making 4 the least value of n.

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