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MATHEMATICS
�Note In a similar manner, it can be shown that if the events E and F are
independent, then
(a)
E′ and F are independent,
(b)
E′ and F′ are independent
Example 14 If A and B are two independent events, then the probability of occurrence
of at least one of A and B is given by 1– P(A′) P(B′)
Solution We have
P(at least one of A and B) = P(A ∪ B)
= P(A) + P(B) − P(A ∩ B)
= P(A) + P(B) − P(A) P(B)
= P(A) + P(B) [1−P(A)]
= P(A)  +  P(B) P(A′)
= 1− P(A′) + P(B) P(A′)
= 1− P(A′)  [1− P(B)]
= 1− P(A′) P (B′)
EXERCISE 13 2
1 If  P(A) 
 53
 and P (B) 
 51
, find P (A  ∩ B) if A and B are independent events