An insurance sales representative sells policies to 5 men, all of identical age and in good health. according to the actuarial tables, the probability that a man of this particular age will be alive 30 years hence is . find the probability that in 30 years (a) all 5 men, (b) at least 3 men, (c) only 2 men, (d) at least 1 man will be alive

(a)

(b)

(c)

(d)

Additional Information:

An information is missing in the given question. The probability that a man of this particular age will be alive 30 years hence is . This additional information will be used to solve the question.

Step-by-step explanation:

Let the probability that one person will be alive in 30 years be p

Let the probability that one person will not be alive in 30 years be q

                                      q = 1 - p

The probability function is;

                               p(x) = ⁿCₓ × pˣ × q⁽ⁿ⁻ˣ⁾                                                        

(a) The probability that all 5 men will be alive in 30 years:

     p(x=5) = ⁵C₅ × ×

                                        = (1 × × 1)

(b) The probability that at least 3 men will be alive in 30 years:

       p(x≥3) = ⁵C₃ × × + ⁵C₄ × × + ⁵C₅ × ×

       p(x≥3) =   (10 × × ) + (5 × × ) + (1 × × 1)

       p(x≥3) + + )

       p(x≥3)

(c) The probability that only 2 men will be alive in 30 years:

     p(x=2) = ⁵C₂ × ×

     p(x=2) = (10 × × )

     p(x=2) =

(d) The probability that at least 1 men will be alive in 30 years:

  p(x≥1) = ⁵C₁ × × × ⁵C₂ × × × ⁵C₃ × × + ⁵C₄ × × + ⁵C₅ × ×

  p(x≥1) = (5 × × ) × (10 × × ) × (10 × × ) + (5 × × ) + (1 × × 1)  

  p(x≥1) + + + +

  p(x≥1)                                

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