If P(A ∩ B) = 0.12 and P(B) = 0.3 for two independent events A and B

1.	If P(A ∩ B) = 0.12 and P(B) = 0.3 for two independent events A and B, then find P(AuB).
Answer» A and B are independent events. ∴ P(A ∩ B) = P(A) – P(B) ∴ 0.12 = P(A) × 0.3 ∴ P(A) = \(\frac{0.12}{0.3}\) = 0.4 Now, according to the law of addition of probability, P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = 0.4 + 0.3 – 0.12 = 0.58

If P(A ∩ B) = 0.12 and P(B) = 0.3 for two independent events A and B, then find P(AuB).

Answer»

A and B are independent events.

∴ P(A ∩ B) = P(A) – P(B)

∴ 0.12 = P(A) × 0.3

∴ P(A) = \(\frac{0.12}{0.3}\) = 0.4

Now, according to the law of addition of probability,

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= 0.4 + 0.3 – 0.12

= 0.58

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If P(A ∩ B) = 0.12 and P(B) = 0.3 for two independent events A and B, then find P(AuB).

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