Question

A pair of dice is thrown and the sum of the numbers appearing on the dice is observed to be 7. Find the probability that the number 5 has appeared on atleast one die.

Answer 1

Let E = event that 5 has appeared on atleast one die

∴  E = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 5), (4, 5), (3, 5), (2, 5), (1, 5)}

Let F = event that sum of no. on die is 7.

∴ F = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}

E ∩ F = {(2, 5), (5, 2)}

∴ n(E ∩ F) = 2

Now, `P(E/F) = (P(E ∩ F))/(P(F)) = (n(E ∩ F))/(n(F)) = 2/6 = 1/3`