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Question

Let P denotes the probability that a man aged x years will die in a year. The probability that out of n men A1,A2,A3,...,An each agedX,A1 will die in a year and will be the first to die is


A

1n[1-(1-p)n]

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B

[1-(1-p)n]

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C

1(n-1)[1-(1-p)n]

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D

None of these

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Solution

The correct option is A

1n[1-(1-p)n]


Explanation for the correct option:

Finding the required probability.

Given: P denotes the probability that a man aged x years will die in a year.

Let Ei be the event that Ai will die in a year where i=1,2,3,4,...,n

The probability that none of A1,A2,A3,...,An dies in a year

=(1pA1).(1pA2),...,(1pAn) where pA1,pA2,...,pAn​​ are the probabilities that A1,A2,A3,...,An dies in a year respectively.

=(1p).(1p),...(1p)=(1p)n

Now the probability that at least one of those dies is A1,A2,A3,...,An=1(1p)n

The probability that among n men A1 is the first one to die is 1n

Therefore, the required probability is

=1n[1(1p)n]

Hence the correct option is (A).


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