An insurance salesman sells policies to 5 men the prob. that a mean will be...

Zerrilloh6

Zerrilloh6

Answered

2021-12-19

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

Answer & Explanation

ol3i4c5s4hr

ol3i4c5s4hr

Expert

2021-12-20Added 48 answers

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(1p)nx;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(123)55
=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(X3)=P(X=3)+P(X=4)+P(X=5)
=(53)(23)3(123)53+(54)(23)4(112)54+(55)(23)5(123)55
=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(123)52
=0.1646
Thus, the probability that in 30 years all only 2 men will be alive is 0.1646.
lovagwb

lovagwb

Expert

2021-12-21Added 50 answers

1) Probability that all men will be alive: P=(23)5=32243.
2) Probability that at least 3 men will be alive: P(x3)=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(x1)=1P(x=0)=1C(5,0)(13)5=242243.
nick1337

nick1337

Expert

2021-12-28Added 573 answers

Step-by-step explanation:
n=5
p=2/3
q=1/3
P(x)=C(n,r)pxqnx
a) P(x=5)=C(5,5)(2/3)5=32/243
b) P(x3)=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(x1)=1P(x=0)=1C(5,0)(1/3)5=242/243

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