Q. 615.0( 1 Vote )

# If P(A) = 0.4, P(B) = 0.8 and P(B | A) = 0.6, then P(A ∪ B) is equal to

A. 0.24

B. 0.3

C. 0.48

D. 0.96

Correct

Answer :

We have,

P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6

We know that,

P(B|A) × P(A) = P(B ∩ A)

⇒ 0.6 × 0.4 = P(B ∩ A)

⇒ P(B ∩ A) = 0.24

Now,

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

[Additive Law of Probability]

= 0.4 + 0.8 – 0.24

= 0.96

Hence, **the correct option is D**

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