Question

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

विकल्प

• 0.24

• 0.3

• 0.48

• 0.96

Answer 1

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