The probabilities that A and B will die within a year are p and q resp

1.	The probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is
Answer» Given that, the probability that A will die = p The probability that B will die = q The probability that only one of them will be alive = P(A∩B’) + P(A’∩B) As, the events are independent, the above form can be written as: P(A∩B’) + P(A’∩B) = P(A).P(B’) + P(A’)P(B) P(A∩B’) + P(A’∩B) = p (1-q) + (1-p)(q) P(A∩B’) + P(A’∩B) = p+q-2pq.

The probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is

Answer»

Given that, the probability that A will die = p

The probability that B will die = q

The probability that only one of them will be alive = P(A∩B’) + P(A’∩B)

As, the events are independent, the above form can be written as:

P(A∩B’) + P(A’∩B) = P(A).P(B’) + P(A’)P(B)

P(A∩B’) + P(A’∩B) = p (1-q) + (1-p)(q)

P(A∩B’) + P(A’∩B) = p+q-2pq.

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The probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is

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