If A and B be mutually exclusive events associated with a random experiment such that P (A) = 0.4 and P (B) = 0.5, then find:(i) P(A ∪ B)(ii) P (A′ ∩ B′)

Home » If A and B be mutually exclusive events associated with a random experiment such that P (A) = 0.4 and P (B) = 0.5, then find:(i) P(A ∪ B)(ii) P (A′ ∩ B′)

If A and B be mutually exclusive events associated with a random experiment such that P (A) = 0.4 and P (B) = 0.5, then find:
(i) P(A ∪ B)
(ii) P (A′ ∩ B′)

If A and B be mutually exclusive events associated with a random experiment such that P (A) = 0.4 and P (B) = 0.5, then find:
(i) P(A ∪ B)
(ii) P (A′ ∩ B′)

A and B are two mutually exclusive events is given to us.

P (A) = 0.4 and P (B) = 0.5

By definition of mutually exclusive events we can write,

P (A ∪ B) = P (A) + P (B)

(i) P (A ∪ B) = P (A) + P (B) = 0.5 + 0.4 = 0.9

(ii) P (A′ ∩ B′) = P (A ∪ B)′ {using De Morgan’s Law}

P (A′ ∩ B′) = 1 – P (A ∪ B)

= 1 – 0.9

= 0.1