Mark the correct alternative in each of the following: If S is the sample space and and S = A ∪ B, where A and B are two mutually exclusive events, then P(A) =

Question

Philoid · Accepted Answer

P(A) = 1/3 P(B) → Given

3 P(A) = P(B) → (1)

Now, since it’s given that A and B are mutually exclusive:

P(A ⋂ B) = 0 → (2)

Now then,

P(S) = P(A⋃B) = 1 → (3)

P(A⋃B) = P(A) + P(B) + P(A⋂B)

P(A) + P(B) = 1 → From (2) & (3)

P(A) + 3 P(A) = 1 → From (1)

4 P(A) = 1

P(A) = 1/4

Mark the correct alternative in each of the following:If S is the sample space and and S = A∪B, where A and B are two mutually exclusive events, then P(A) =

Mark the correct alternative in each of the following:
If S is the sample space and and S = A∪B, where A and B are two mutually exclusive events, then P(A) =