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  • The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate .P(A)+P(B)

The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate P(\bar{A})+P(\bar{B}) .

Answers (1)

Given-

At least one of the two events A and B occurs is 0.6 i.e. P(A\cupB) = 0.6

If A and B occur simultaneously, the probability is 0.3 i.e. P(A\capB) = 0.3

It is known to us that

P(A\cupB) = P(A)+ P(B) – P(A\capB)

\Rightarrow  0.6 = P(A)+ P(B) – 0.3
\Rightarrow  P(A)+ P(B) = 0.6+ 0.3 = 0.9

To find- P(\bar{A})+P(\bar{B})

Therefore,

\\ P(\bar{A})+P(\bar{B})=[1-P(A)+1-P(B)] \\ \Rightarrow P(\bar{A})+P(\bar{B})=2-[P(A)+P(B)] \\ \Rightarrow P(\bar{A})+P(\bar{B})=2-0.9 \\ P(\bar{A})+P(\bar{B})=1.1

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