If the probability that a problem will be solved by three people is 1 2 1 3 and 1 6 then what is the...........

Quantitative Aptitude ( CCS) Probability

If the probability that a problem will be solved by three people is 1/2, 1/3 and 1/6, then what is the probability that the problem will be solved?

13/14

11/12

13/18

7/12

Let the probabilities be P(A)=1/2 P(B)=1/3 and P(C)=1/6

We need to find the Union of these 3 independent events i.e P( A or B or C)

so P(AUBUC)=P(A)+P(B)+P(C)-P(AB)-P(BC)-P(CA)+P(ABC)

=(1/2)+(1/3)+(1/6)-((1/2)*(1/3))-((1/3)*(1/6))-((1/6)*(1/2))+((1/2)*(1/3)*(1/6))

=(1/2)+(1/3)+(1/6)-(1/6)-(1/18)-(1/12)+(1/36)

=(5/6)-(5/36)+(1/36)

=26/36=13/18

Hence, option 3 is the correct answer.

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