HW 29 A utility company might offer electrical rates based o

HW 2.9. A utility company might offer electrical rates based on time-of-day consumption to decrease the peak demand in a day. Enough customers need to accept the plan for it to be successful. Suppose that among 50 major customers, 15 would accept the plan. The utility selects 10 major customers randomly (without replacement) to contact and promote the plan. a) What is the probability that exactly two of the selected major customers accept the plan? (b) What is the probability that at least one of the selected major customers accepts the plan?

Solution

a)

There are 50C10 = 10272278170 ways to select 10 customers.

There are (35C8)(15C2) = 2471261100 ways to select a group of 10 in which 8 would not accept, and 2 will accept.

hence

P(2 will accept) = 2471261100 / 10272278170 = 0.240575757 [ANSWER]

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b)

P(at least one accepts) = 1 - P(no one accepts)

There are 35C10 = 183579396 ways to select 10 customers who will not accept.

hence,

P(no one accepts) = 183579396 / 10272278170 = 0.017871342

Thus,

P(at least one accepts) = 0.982128658 [answer]