NCERT Class XII Mathematics Chapter - - Solutions
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Question : 35
Total: 101
Two events A and B will be independent, if
Solution:
A and B are independent ⇒ P(A ∩ B) = P(A) P(B)
and P(A′ ∩ B′) = P(A ∪ B)′ = 1 – P(A ∪ B) = 1 – {P(A) + P(B) – P(A ∩ B)}
= 1 – P(A) – P(B) + P(A)P(B) = (1 – P(A))(1 – P(B))
and P(A′ ∩ B′) = P(A ∪ B)′ = 1 – P(A ∪ B) = 1 – {P(A) + P(B) – P(A ∩ B)}
= 1 – P(A) – P(B) + P(A)P(B) = (1 – P(A))(1 – P(B))
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