Question

A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8 ,given that the red die resulted in a number less than 4
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Answer 1

Explanation:

Let, the 1st observation be from the black die

the 2nd observation be from the red die

When two dice (one black and another red) are rolled then, the sample space (S) has 6 × 6 = 36 number of elements.

E is the sum of the observations = 8

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

F is the red die resulted in a number less than 4

{(1,1) , (1,2) , (1,3) , (2,1) , (2,2) , (2,3) , (3,1) , (3,2) , (3,3) , (4,1) , (4,2) , (4,3) , (5,1) , (5,2) , (5,3) , (6,1) , (6,2) , (6,3)}

∴ E ∩ F = {(5,3) , (6,2)}

P(F) = 18/36 and P(E ∩ F) = 2/36

The conditional probability of obtaining the sum equal to 8, given that the red die resulted in a number less than 4, is given by P(E|F)

Hence, P(E|F) = P(E ∩ F) / P(F)

= 2/36 / 18/36

= 2/18

= 1/9