If S is the sample space and P(A) = \(\cfrac13P(B)\) and S = A ∪ B,

1.	If S is the sample space and P(A) = \(\cfrac13P(B)\) and S = A ∪ B, where A and B two mutually exclusive events, then P(A) =A. 1/4B. 1/2C. 3/4D. 3/8
Answer» Correct option is A. 1/4 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

If S is the sample space and P(A) = \(\cfrac13P(B)\) and S = A ∪ B, where A and B two mutually exclusive events, then P(A) =A. 1/4B. 1/2C. 3/4D. 3/8

Answer»

Correct option is A. 1/4

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

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If S is the sample space and P(A) = \(\cfrac13P(B)\) and S = A ∪ B, where A and B two mutually exclusive events, then P(A) =A. 1/4B. 1/2C. 3/4D. 3/8

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