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. P (A) = 0.3, P (B) = 0.5 and P (A ∪ B) = 0.5 Now 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) So, 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) is 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.

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

Now 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)

So, 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) is 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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