Question

A pair of dice are thrown, what is the probability of throwing at least one 2? What is the probability of throwing a total less than or equal to 9?

Answer 1

Number of possibilities in throwing a dice = 6 (1, 2, 3, 4, 5, 6)

Probability of throwing a number P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = 1/6

Probability of throwing at least one 2 = Probability of throwing both 2's + Probability of throwing a 2 and any other number on the other dice = (1/6)(1/6) + (1/6)(5/6) = 6/36 = 1/6

Number of combinations where the total is less than 9 are --> (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (5,1) (5,2) (5,3) (5,4) (6,1) (6,2) (6,3) --> 30
Total number of combinations in throwing 2 dice = 6*6 = 36
Hence, probability of throwing a total of less than equal to 9 = 30/36 = 5/6