Question

A black and a red dice are rolled. 

Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

Answer 1

The sum of the reserves on the E event dice is assumed to be 8, and the number shown on the F event red die has a compatibility of less than 4.

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

F = {(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)}

Total types = 18

E ∩ F = {(2, 6), (3, 5)}

P(E ∩ F) = `2/36 = 1/18`

P(F) = `18/36 = 1/2`

P(E|F) = `(P(E ∩ F))/(P(F))`

=`1/18 ÷ 1/2`

=`1/9`