Statistics And Probability Question 457
Question: 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
[CEE 1993; Pb. CET 2004]
Options:
A) $ p+q $
B) $ p+q-2qp $
C) $ p+q-pq $
D) $ p+q+pq $
Show Answer
Answer:
Correct Answer: B
Solution:
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Required probability is P[(A will die and $ B $ alive) or (B will die and $ A $ alive)] $ =P[(A\cap {B}')\cup (B\cap {A}')] $ Since events are independent, so Required probability $ =P(A)\,.\,P({B}')+P(B)\,.\,P({A}') $ $ =p\,.\,(1-q)+q(1-p)=p+q-2pq. $
BETA
