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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 to A. 0.24 B. 0.3 C. 0.48 D. 0.96

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

Answers (1)

Solution

Given-   

P(A) = 0.4, P(B) = 0.8 and P(B \vert A) = 0.6   

It is known that,   

\\P(B \vert A) \times P(A) = P(B \cap A) \\ \Rightarrow 0.6 \times 0.4 = P(B \cap A) \\ \Rightarrow P(B \cap A) = 0.24 \\P(A \cup B) = P(A) + P(B) - P(A \cap B)$ [Additive Law of Probability] $\\= 0.4 + 0.8 - 0.24 \\= 0.96

Hence, correct option is D.

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infoexpert22

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