For two events A and B of a sample space S, if P(A) = 3/8, P (B) = 1/2

1.	For two events A and B of a sample space S, if P(A) = 3/8, P (B) = 1/2 and P(A ∪ B) = 5/8, Find the value of the following.(a) P(A ∩ B) (b) P(A’ ∩ B’) (c) P(A’ ∪ B’)
Answer» Here, P(A) = 3/8, P (B) = 1/2, P(A ∪ B) = 5/8 (a) P(A ∪ B) = P(A) + P(B) – P(A ∩ B) ∴ P(A ∩ B) = P(A) + P(B) – P(A ∪ B) = 3/8 + 1/2 - 5/8 = 1/4 (b) P(A’ ∩ B’) = P(A ∪ B)’ = 1 – P(A ∪ B) = 1- 5/8 = 3/8 (c) P(A’ ∪ B’) = P(A ∩ B)’ = 1 – P(A ∩ B) = 1- 1/4 = 3/4

For two events A and B of a sample space S, if P(A) = 3/8, P (B) = 1/2 and P(A ∪ B) = 5/8, Find the value of the following.(a) P(A ∩ B) (b) P(A’ ∩ B’) (c) P(A’ ∪ B’)

Answer»

Here, P(A) = 3/8, P (B) = 1/2, P(A ∪ B) = 5/8

(a) P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

∴ P(A ∩ B) = P(A) + P(B) – P(A ∪ B)

= 3/8 + 1/2 - 5/8

= 1/4

(b) P(A’ ∩ B’) = P(A ∪ B)’

= 1 – P(A ∪ B)

= 1- 5/8

= 3/8

(c) P(A’ ∪ B’) = P(A ∩ B)’

= 1 – P(A ∩ B)

= 1- 1/4

= 3/4

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For two events A and B of a sample space S, if P(A) = 3/8, P (B) = 1/2 and P(A ∪ B) = 5/8, Find the value of the following.(a) P(A ∩ B) (b) P(A’ ∩ B’) (c) P(A’ ∪ B’)

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