Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6.

Find


(i) P(A and B) (ii) P(A and not B)


(iii) P(A or B) (iv) P(neither A nor B)


Given: P(A) = 0.3, P(B) = 0.6.

(i) P(A and B)


As A and B are independent events.


P(A and B) = P (A B) = P(A) . P(B)


= 0.3 × 0.6


= 0.18


(ii) P(A and not B)


P(A and not B) = P (A B) = P(A) - P(A B)


= 0.3 - 0.18


= 0.12


(iii) P(A or B)


P(A or B) = P(A B)


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


P (A B) = 0.3 + 0.6 – 0.18


P (A B) = 0.72


(iv) P(neither A nor B)


P(neither A nor B) = P(A B)


As, { A B =(A B)}


P(neither A nor B) = P ((A B))


= 1 - P (A B)


= 1 - 0.72


= 0.28


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