Question

4. A pair of fair dice is rolled repeatedly. Calculate the probability that the first prime sum occurs on the fifth roll. Facts: a prime number is divisible only by itself and 1…2 is a prime number.

Answer 1

The following sums are possible when a pair of dice is rolled.

{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Prime numbers among the possible sums are,

{2, 3, 5, 7, 11}

P(sum is 2) = 1/36

P(sum is 3) = 2/36

P(sum is 5) = 4/36

P(sum is 7) = 6/36

P(sum is 11} = 2/36

P(prime sum) = 1/36 + 2/36 + 4/36 + 6/36 + 2/36

= 5/12

P(not a prime sum) = 1 - 5/12 = 7/12

P(first prime sum occurs on the fifth roll) = P(no prime sum on first 4 rolls) x P(prime some on 5th roll)

= (7/12)⁴ x (5/12)

= 0.0482