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Question

The probability of happening at least one of the events A and B is 0.6. If the events Aand B happens simultaneously with the probability 0.2, then PA'+PB'=


A

0.4

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B

0.8

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C

1.4

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D

1.2

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Solution

The correct option is D

1.2


Calculate the required probability

Given, the probability that atleast one of the events A,B happens is PAB

So, PAB=0.6

Also, the probability of simultaneous happening is PAB

then PAB=0.2

Now we know that ,PAB=PA-PAB+PB

PAB=PA-PAB+PBPA+PB=PAB+PABPA+PB=0·6+0·2PA+PB=0.8

Now ,PA+PA'=1and PB+PB'=1

1-PA'+1-PB'=0.82-PA'-PB'=0.8PA'+PB'=2-0.8PA'+PB'=1.2

Therefore, PA'+PB'=1.2, so option (D) is the correct answer.


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