Let p be the probability that a man aged x years will die in a year time. The probability that out o

Question

Let p be the probability that a man aged x years will die in a year time. The probability that out of ′n′ men A₁, A₂, A₃,......, A_n each aged ′x′ years. A₁ will die & will be the first to die is:

Accepted Answer

P = P(1 person lies) + P(2 person lies) P(A 1 lies
first / 2 person lied) + P(3 person lied)
P(A 1 died first / 3 person lied)
= ⁿC₁ pq^n-1 × + ⁿC₁ p² q^n-2 × + ⁿC₂ p³q^n-3 × + ....
= pq^n-1 + ^n-1C_r-1 p²q^n-2 + ⁿC₃ p³q^n-3 + .....
= pq^n-1 +
P = Pq^n-1 +
⇒ P = pq^{n - 1} + (1 - ⁿC₀ p⁰ q^{n - n}C₁ P¹ q^n-1)
P = Pq^n-1 + (1 - qⁿ - nPq^n-1) =

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