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 isQuestion 8Answera.13/15b.11/15c.Noned.13/15
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 isQuestion 8Answera.13/15b.11/15c.Noned.13/15
Solution
The probability that only one of them will be alive at the end of the year can be calculated as the sum of two probabilities:
- The probability that A will die and B will live.
- The probability that B will die and A will live.
The probability that A will die and B will live is calculated by multiplying the probability that A will die (p) by the probability that B will live (1-q).
Similarly, the probability that B will die and A will live is calculated by multiplying the probability that B will die (q) by the probability that A will live (1-p).
So, the total probability that only one of them will be alive at the end of the year is p*(1-q) + q*(1-p).
Unfortunately, without knowing the values of p and q, we cannot determine the exact probability and match it to the options provided (a.13/15, b.11/15, c.None, d.13/15).
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