Explanation
1. Probability of "At Least One" Death
First, we calculate the probability that at least one person out of the n individuals dies within the year.
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Probability that a person survives =1−p
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Probability that all n people survive =(1−p)n
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Probability that at least one person dies =1−(1−p)n
2. Distributing the Probability among n individuals
If we are looking for the probability that a specific person (A1) is the one represented in the group's "death event," we consider the symmetry of the group. Since all n people are of the same age and have the same initial probability p, they are equally likely to be the one who dies.
To find the individual share of the "at least one death" probability for A1:
P(A1 dies)=n1×P(At least one person dies)
3. Final Calculation
Substitute the value from Step 1:
Final Answer
By considering the probability of the event occurring within the group and assigning the specific likelihood to A1, we arrive at:
Correct Option: (C) n1[1−(1−p)n]
