An insurance salesman sells policies to 5 men the prob. that a mean will be a live in 30 years is 23. Find the prob. that in 30 years: a) all 5 men , b) at least 3 men , c) only 2 men

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ol3i4c5s4hr · Accepted Answer

Let X be the number of men will be alive and n be sample number of men.  From the given information, probability that a men will be alive in 30 years is 23 and n=5.  Here, men are independent and probability of success is constant. Hence, X follows binomial distribution with parameters n=5 and p=23.  The probability mass function of binomial random variable X is  P(X=x)=(nx)px(1−p)n−x;x=0,1,...,n  Step 3  a. The probability that in 30 years all 5 men will be alive is  P(X=5)=(55)(23)5(1−23)5−5  =0.1317  Thus, the probability that in 30 years all 5 men will be alive is 0.1317.  Step 4  b. The probability that in 30 years at least 3 men will be alive is  P(X≥3)=P(X=3)+P(X=4)+P(X=5)  =(53)(23)3(1−23)5−3+(54)(23)4(1−12)5−4+(55)(23)5(1−23)5−5  =0.3292+0.3292+0.1317  =0.7901  The probability that in 30 years at least 3 men will be alive is 0.7901.  Step 5  c. The probability that in 30 years all only 2 men will be alive is  P(X=2)=(52)(23)2(1−23)5−2  =0.1646  Thus, the probability that in 30 years all only 2 men will be alive is 0.1646.

lovagwb · Accepted Answer

1) Probability that all men will be alive: P=(23)5=32243.   2) Probability that at least 3 men will be alive: P(x≥3)=C(5,3)⋅(23)3⋅(13)2+C(5,4)⋅(23)4⋅(13)1+C(5,5)⋅(23)5=80243+80243+32243=192243.   3) Only two men will be alive: P(x=2)=C(5,2)⋅(23)2⋅(13)3=40243.   4) At least 1 man will be alive: P(x≥1)=1−P(x=0)=1−C(5,0)⋅(13)5=242243.

nick1337 · Accepted Answer

Step-by-step explanation: n=5 p=2/3 q=1/3 P(x)=C(n,r)⋅px⋅qn−x a) P(x=5)=C(5,5)⋅(2/3)5=32/243 b) P(x≥3)=C(5,3)⋅(2/3)3⋅(1/3)2+C(5,4)⋅(2/3)4⋅(1/3)1+C(5,5)⋅(2/3)5=192/243 c) P(x=2)=C(5,2)⋅(2/3)2⋅(1/3)3=40/243 d) P(x≥1)=1−P(x=0)=1−C(5,0)⋅(1/3)5=242/243

An insurance salesman sells policies to 5 men the prob.

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