Probability Practice Test 2

Question : 33 of 37

Marks: +1, -0

If 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

p + q
p + q – 2pq
p + q – pq
p + q + pq

Validate

Solution:

P (only one of A and B will die in a year)

=P(\ov A B)+P(A \ov B)

=P(\ov A)P( B)+P(A)P( \ov B)

[Since A and B are independent]
= (1 – p)q + p (1 – q)
= p + q – 2pq.

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