An insurance company found that 25% of all insurance policies are terminated before their maturity date. Assume that 15 policies are randomly selected from the company's policy database.
(a)what is the probability that more than 8 but less than 11policies are terminated before maturing? (2)
(b)what is the probability that is not least 14 is terminated before maturity? (2)
Answers
Given : An insurance company found that 25% of all insurance policies are terminated before their maturity date . 15 policies are randomly selected from the company's policy database.
To find : probability that more than 8 but less than 11 policies are terminated before maturing
Solution:
An insurance company found that 25% of all insurance policies are terminated before their maturity date
=> Probability of policy termination p = 25/100 = 1/4
Probability of policy not terminating = 1 - 1/4 = 3/4
15 policies are randomly selected => n = 15
p(x) = ⁿCₓpˣqⁿ⁻ˣ
probability that more than 8 but less than 11 policies are terminated before maturing
=> x = 9 , 10
=> probability = p(9) + p(10)
= ¹⁵C₉(1/4)⁹(3/4)⁶ + ¹⁵C₁₀(1/4)¹⁰(3/4)⁵
= ( 3⁵ / 4¹⁵) ( 5005 * 3 + 3003 )
= ( 3⁵ / 4¹⁵) ( 18018 )
= 0.0041
= 0.41 % is the probability that more than 8 but less than 11 policies are terminated before maturing
probability that at least 14 is terminated before maturity
= 1 - 15 terminated before maturity
= 1 - ¹⁵C₁₅(1/4)¹⁵(3/4)⁰
= 1 - 0.0000000009
≈ 1
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