Question

A pair of dice is cast. What is the probability that the sum of the two number landing uppermost is less than 5, if it is known that the sum of the numbers falling uppermost is less than 7?

Answer 1

Total sample space = 6 * 6 = 36

Sample space for sum of two numbers less than 7 = {(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)}

Sample sapce for sum of two numbers less than 5 = {(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)}

P(sum of two numbers less than 5 | sum of two numbers less than 7) = P(sum of two numbers less than 5) / P(sum of two numbers less than 7)

                                                                  = (6/36) / (15/36)

                                                                  = 6/15

                                                                  = 0.4 (ans)