NCERT Class XII Mathematics Chapter - - Solutions
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Question : 25
Total: 101
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).
Solution:
Since A and B be independent events
(i) P(A ∩ B) = P(A) × P(B) = 0.3 × 0.4 = 0.12.
(ii) P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = P(A) + P(B) – P(A) P(B) = 0.3 + 0.4 – (0.3 × 0.4) = 0.7 – 0.12 = 0.58.
(iii) P(A | B)=
=
= P ( A ) = 0.3
(iv) P(B | A)=
=
= P ( B ) = 0.4
(i) P(A ∩ B) = P(A) × P(B) = 0.3 × 0.4 = 0.12.
(ii) P(A ∪ B) = P(A) + P(B) – P(A ∩ B) = P(A) + P(B) – P(A) P(B) = 0.3 + 0.4 – (0.3 × 0.4) = 0.7 – 0.12 = 0.58.
(iii) P(A | B)
(iv) P(B | A)
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