Question

an insurance agent meets twelve potential customers independently, each of whom is equally likely to purchase an insurance product. six are interested only in auto insurance, four are interested only in homeowners insurance, and two are interested only in life insurance. the agent makes six sales. calculate the probability that two are for auto insurance, two are for homeowners insurance, and two are for life insurance.

Answer 1

The probability of customers buying each insurance is 1/24.

What is probability?

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

Total number of sales is 6.

Total number of customers is 12.

The number of customers interested only in auto insurance is 6.

The number of customers interested only in homeowners insurance is 4.

The number of customers interested only in life insurance is 2.

Now, the probability that two sales are for auto insurance is given as,

2/6 = 1/3

The probability that two sales are for homeowners insurance is given as,

2/4 = 1/2

And,  the probability that two sales are for life  insurance is given as,

2/4 = 1/2

Thus the probability of two sales for each insurance is given as the product of all the three probabilities as,

 1/3 × 1/2 × 1/2 = 1/12

And, the probability of six customers out of 12  buying the sales is,

6/12 = 1/2

Thus, the probability for the given case is,

1/2 × 1/12 = 1/24

Hence, the probability for the given problem is 1/24.

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