Question

A black and a red dice are rolled. 

Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.

Answer 1

Let x denote the outcome on the black die and y denote the outcome on the red die, then sample space is

S = {(x, y): x, y ∈ (1, 2, 3, 4, 5, 6)}, which contain 6 × 6 = 36 equally likely simple events.

E: 'sum greater than 9' and F: 'black die resulted in a 5'

E = {(6, 4), (4, 6), (5, 5), (5, 6), (6, 5), (6, 6)}

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

⇒ E ∩ F = {(5, 5), (5, 6)}

`P (E) = 6/36, P(F) = 6/36, P (E cap F) = 2/36`

Required probability= P(E|F)

`(P(E cap F))/(P(F)) = (2/36)/(6/36)`

`= 2/6 = 1/3`