If P(A) = 0.4, P(B) = p, P(A ∪ B) = 0.6 and A and B are given to be

1.	If P(A) = 0.4, P(B) = p, P(A ∪ B) = 0.6 and A and B are given to be independent events, find the value of ‘p’.
Answer» P(A ∪ B) = P(A) + P(B) – P(A ∩ B) ⇒ 0.6 = 0.4 + p – P(A ∩ B) ⇒ P(A ∩ B) = 0.4 + p – 0.6 = p – 0.2 Since, A and B are independent events. ∴ P(A ∩ B) = P(A) × P(B) ⇒ p – 0.2 = 0.4 × p ⇒ p – 0.4 p = 0.2 ⇒ 0.6 p = 0.2 ⇒ p = \(\frac{0.2}{0.6}\) = \(\frac{1}{3}\)

If P(A) = 0.4, P(B) = p, P(A ∪ B) = 0.6 and A and B are given to be independent events, find the value of ‘p’.

Answer»

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

⇒ 0.6 = 0.4 + p – P(A ∩ B)

⇒ P(A ∩ B) = 0.4 + p – 0.6 = p – 0.2

Since, A and B are independent events.

∴ P(A ∩ B) = P(A) × P(B)

⇒ p – 0.2 = 0.4 × p

⇒ p – 0.4 p = 0.2

⇒ 0.6 p = 0.2

⇒ p = \(\frac{0.2}{0.6}\) = \(\frac{1}{3}\)

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If P(A) = 0.4, P(B) = p, P(A ∪ B) = 0.6 and A and B are given to be independent events, find the value of ‘p’.

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