Question

Suppose that we have a sample space with six equally likely experimental outcomes: x1, x2, x3, x4, x5, x6, and that A = { x2, x3, x5} and B = { x1, x2} and C= {x1, x4, x6}, then P(A ∩ B) =

Answer 1

Solution :

Probability of an event E is given as follows :

Where, n(E) is the number of outcomes favourable to the event E and n(S) is the total number of outcomes in the sample space.

Hence,

Where, n(A ∩ B) is the number of outcomes which are present in both of A and B. n(S) is the total number of outcomes in the sample space.

Since, only the outcome x2 is present in both of A and B, therefore n(A ∩ B) = 1

n(S) = 6

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