Question

Two unbiased dice are thrown. Find the probability that the sum of the numbers appearing is 8 or greater, if 4 appears on the first die.

Answer 1

It is given that two unbiased dice are thrown

So the outcome = 6² = 36

Consider P (A) as the probability of getting a sum greater than 8

Consider P (B) as the probability of getting 4 on the first die

Sample space of B = {(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)}

P (B) = 6/36 = 1/6

Consider P (A ∩ B) as the probability of getting 4 on the first die and the sum greater than or equal to 8

Sample space (A ∩ B) = {(4, 4), (4, 5), (4, 6)}

P (A ∩ B) = 3/36 = 1/12

Here the probability that sum of the numbers is greater than or equal to 8 given that 4 was thrown first