A utility company might offer electrical rates based on time-of-day consumption

Question

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. What is the probability that exactly two of the selected major customers accept the plan? What is the probability that at least one of the selected major customers accepts the plan? Instead of 15 customers, what is the minimum number of major customers that would need to accept the plan to meet the following objective? The probability that at least 1 selected major customer accepts the plan is greater than or equal to 0.95.

Explanation / Answer

Solution:

a)There are 50C10 = 10272278170 ways to choose 10 customers.

There are 15C2 = 105 ways to choose two who will accept.

There are 35C8 = 23535820 ways to choose 8 who will not accept.

Thus, there are 105*23535820 = 2471261100 ways to do the description.

hence,

P = 2471261100 / 10272278170 = 0.240575757

b) P(at least one) = 1 - P(none accepts)

So, there are 35C10 = 183579396 ways to choose 10 who will not accept.

hence,

P(none accepts) = 183579396/10272278170 = 0.01787134

Thus,

P(at least one accepts) = 0.982128658

c) It is known that the probability that at least 1 selected major customer accepts the plan is greater than or equal to 0.95

P(X1)=0.95

The minimum no of customers accept plan to meet the objective is calculated as follows:0.05

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