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  • The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then P ( A) + P (B ) is A. 0.4 B. 0.8 C. 1.2 D. 1.6

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then P (\bar{A}) + P (\bar{B}) is
A. 0.4
B. 0.8
C. 1.2
D. 1.6

Answers (1)

Given:

P ( at least one of A or B occurs) = 0.6, thus, P (A U B) = 0.6

& P (A & B occurs simultaneously) = 0.2, thus, P (A ∩ B) = 0.2

Now, P (A U B) = P (A) + P (B) – P (A ∩ B)        ……. (by general addition rule)

Thus, P (A) + P (B) – 0.2 = 0.6

P (A) + P (B) = 0.6 + 0.2

P (A) + P (B) = 0.8

Now,

P (A) = 1 – P (A’)           ……… by complement rule

Similarly, P (B) = 1 – P (B’)         

Therefore,

1 – P (A’) + 1 – P (B’) = 0.8

2 – [P (A’) + P (B’)] = 0.8

2 – 0.8 = P (A’) + P (B’)

P (A’) + P (B’) = 1.2

Thus, option C is the correct answer.

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