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If the probability 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
- a)p + q
- b)p + q - 2pq
- c)p + q -pq
- d)p + q + pq
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the probability that A and B will die within a year are p and q res...
Solution:
Let's consider the events:
A: The event that A dies within a year.
B: The event that B dies within a year.
To find the probability that only one of them will be alive at the end of the year, we need to find the probability of the following two events:
1. A dies and B doesn't die
2. B dies and A doesn't die
The probability of A dying and B not dying is given by:
p(1-q)
Similarly, the probability of B dying and A not dying is given by:
q(1-p)
Therefore, the probability that only one of them will be alive at the end of the year is given by the sum of these two probabilities:
p(1-q) + q(1-p)
= p + q - 2pq
Hence, option 'B' is the correct answer.
Let's consider the events:
A: The event that A dies within a year.
B: The event that B dies within a year.
To find the probability that only one of them will be alive at the end of the year, we need to find the probability of the following two events:
1. A dies and B doesn't die
2. B dies and A doesn't die
The probability of A dying and B not dying is given by:
p(1-q)
Similarly, the probability of B dying and A not dying is given by:
q(1-p)
Therefore, the probability that only one of them will be alive at the end of the year is given by the sum of these two probabilities:
p(1-q) + q(1-p)
= p + q - 2pq
Hence, option 'B' is the correct answer.
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If the probability that A and B will die within a year are p and q res...
Either person 1 dies and person 2 lives, or the other way. So, required probability is p(1-q) + (1-p)q
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If the probability 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, isa)p + qb)p + q - 2pqc)p + q -pqd)p + q + pqCorrect answer is option 'B'. Can you explain this answer?
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