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Question
If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) is equal to ______.
Options
0.24
0.3
0.48
0.96
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Solution
If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) is equal to 0.96.
Explanation:
Given that: P(A) = 0.4
P(B) = 0.8
And `"P"("B"/"A")` = 0.6
`"P"("B"/"A") = ("P"("A" ∩ "B"))/("P"("A"))`
⇒ 0.6 = `("P"("A" ∩ "B"))/0.4`
∴ P(A ∩ B) = 0.6 × 0.4 = 0.24
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= 0.4 + 0.8 – 0.24
= 1.20 – 0.24
= 0.96
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