If A and B are two events associated with a random experiment such tha

1.	If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.4 and P(A∪ B) = 0.5, find P(A ∩ B).
Answer» Given A and B are two events And, P(A) = 0.3 P(B) = 0.5 P(A ∪ B) = 0.5 We need to find P(A ∩ B). By definition of P(A or B) under axiomatic approach(also called addition theorem) we know that: P(A ∪ B) = P(A) + P(B) – P(A ∩ B) ∴ P(A ∩ B) = P(A) + P(B) – P(A ∪ B) ⇒ P(A ∩ B) = 0.3 + 0.4 – 0.5 = 0.7 – 0.5 = 0.2 ∴ P(A ∩ B) = 0.2

If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.4 and P(A∪ B) = 0.5, find P(A ∩ B).

Answer»

Given A and B are two events

And, P(A) = 0.3 P(B) = 0.5 P(A ∪ B) = 0.5

We need to find P(A ∩ B).

By definition of P(A or B) under axiomatic approach(also called addition theorem) we know that:

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

∴ P(A ∩ B) = P(A) + P(B) – P(A ∪ B)

⇒ P(A ∩ B) = 0.3 + 0.4 – 0.5 = 0.7 – 0.5 = 0.2

∴ P(A ∩ B) = 0.2

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If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.4 and P(A∪ B) = 0.5, find P(A ∩ B).

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