Question

The probability that at least 2 of 3 people a, b and c will survive for 10 years is 247/315. the probability that a alone will survive for 10 years is 4/105 and the probability that c alone will die within 10 years is 2/21. assuming that the events of the survival of a, b and c can be regarded as independent, calculate the probability of surviving 10 years for each person.

Answer 1

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Maths

For any three events A,B and C we have

P (at least one of A,B and C occurs)

P (at least two of A,B,C occur)

P (exactly two of A,B,C occur)

P (exactly one of A,B,C occurs)



Answer

 P (at least one of A,B and C occurs)= P(A)+P(B)+P(C)−P(A∩B)−P(B∩C)−P(C∩A)+P(A∩B∩C)

P (at least two of A,B and C occurs) =P(B∩C)+P(C∩A)+P(A∩B)−2P(A∩B∩C)

P (exactly two of A,B and C occurs) =P(B∩C)+P(C∩A)+P(A∩B)−3P(A∩B∩C)

P (exactly one of A,B and C occurs) =P(A)+P(B)+P(C)−2P(B∩C)−2P(C∩A