Q. 1 A5.0( 1 Vote )

# 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)

(iii)

(iv)

Answer :

Given A and B are two mutually exclusive events

And, P(A) = 0.4 P(B) = 0.5

By definition of mutually exclusive events we know that:

P(A ∪ B) = P(A) + P(B)

We have to find-

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

iii) P(A’ ∩ B) = This indicates only the part which is common with B and not A ⇒ This indicates only B.

P(only B) = P(B) – P(A ∩ B)

As A and B are mutually exclusive So they don’t have any common parts ⇒ P(A ∩ B) = 0

∴ P(A’ ∩ B) = P(B) = 0.5

iv) P(A ∩ B’) = This indicates only the part which is common with A and not B ⇒ This indicates only A.

P(only A) = P(A) – P(A ∩ B)

As A and B are mutually exclusive So they don’t have any common parts ⇒ P(A ∩ B) = 0

∴ P(A ∩ B’) = P(A) = 0.4

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