Q8 of 105 Page 546

Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find

(i) P(A ∩ B) (ii) P(A ∪ B)


(iii) P (A|B) (iv) P (B|A)

Given: P(A) = 0.3 and P(B) = 0.4

(i) P(A ∩ B)


When A and B are independent.


⇒ P (A ∩ B) = P(A) . P(B)


⇒ P (A ∩ B) = 0.3 × 0.4


⇒ P (A ∩ B) = 0.12


(ii) P(A ∪ B)


As we know, P (A ∪ B) = P(A) + P(B) - P (A ∩ B)


⇒ P (A ∪ B) = 0.3 + 0.4 – 0.12


⇒ P (A ∪ B) = 0.58


(iii) P (A|B)


As we know


⇒


⇒ P (A|B) = 0.3


(iv) P (B|A)


As we know


⇒


⇒ P (B|A) = 0.4


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