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

1.	If P(A) = 0.4, P(B) = 0.8 and P(B \| A) = 0.6, then P(A ∪ B) is equal toA. 0.24B. 0.3C. 0.48D. 0.96
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.

If P(A) = 0.4, P(B) = 0.8 and P(B | A) = 0.6, then P(A ∪ B) is equal toA. 0.24B. 0.3C. 0.48D. 0.96

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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If P(A) = 0.4, P(B) = 0.8 and P(B | A) = 0.6, then P(A ∪ B) is equal toA. 0.24B. 0.3C. 0.48D. 0.96

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