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1. Customers who are registered on a corporate web site are summarized by the type of shipping contract they use and the number of orders in the previous month. The number of customers in each category are shown in the following table Shipping Contract No orders One order More than one order 40 Total Express 25 65 Standard 15 45 20 80 40 110 60 210 130 (a) If customers are selected at random without replacement, how many unique samples of eight express and ten standard customers are possible? Order does not matter. (2 pts) (b) Suppose 10 express and 15 standard customers are selected without replacement. What is ability of selecting exactly one express customer with no orders last month and exactly one standard customer with no orders last month? (3 pts) (c) Suppose that three customers are selected randomly, without replacement, for a survey What is the probability that at least two selected customers use express shipping? (4pts) (d) What is the probability that a randomly selected customer uses standard shipping or had no orders? (4 pts)

math   Statistics-And-Probability   
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a)Given that the customers are selected at random, the number of unique samples of selecting eight express and ten standard customers are, The number of favourable cases of selecting 8 express customers out of 130 express customers is 130CB The number of favourable cases of selecting 10 standard customers out of 80 express customers is 80C10 The number of unique samples of selecting eight express and ten standard customers are 130Cg80C10 b)Given that 10 express and 15 standard customers are selected without replacement, the probability of selecting one express customer with no orders last month and exactly one standard customer with no orders last month is Number of express customer with no orders last month is 25 Number of express customer with no orders last month is 15 exhaustive number of cases 210c25 (Since 25 customers are to be selected from 210 customers) favourable number of cases 2 I *4 Required probability favourable number of cases exhaustive number of cases 25c 105c 15c 65 25C 105C9210C25 0.000972From 10 express and 15 standard customers selected without replacement, the probability of selecting one express customer with no orders last month and exactly one standard customer with no orders last month is 0.000972 c)Given that three customers are selected randomly without replacement, the probability that at least two selected customers uses express shipping is P(at least 2 selected customers uses express shipping) P( 2 or more selected customers uses express shipping) -P( 2 selected customers uses express shipping) +P( 3 selected customers uses express shipping) 180 1130C 210 210 C3 C3 130.129 80 210+209-205 130-129-128 09 208 3 2 1 3 2+1 670800 357760 0.4408750.2351330.676008 1521520 1521520 From the three customers selected randomly without replacement, the probability that at least two selected customers uses express shipping is 0.676008 d) The probability that a randomly selected customer uses standard shipping or had no orders A event of randomly selecting a customer who uses standard shippingP(A) = n(d where n(A) is the favourable number of cases and n(S) is the exhaustive number of cases 8- event of randomly selecting a customer who had no orders P(B) = n(S)-210 The probability that a randomly selected customer uses standard shipping or had no orders is ) n(S) 210 n(B) 40 P(AUB) P(A) P(B) - P(AnB) The probability that a randomly selected customer uses standard shipping and had no orders is n(S) 210 P(A U B) = P(A) + P(B)--P(An B) 80 40 15 105 210 210 210 210 P(AUB) = 0.5The probability that a randomly selected customer uses standard shipping or had no orders is 0.5

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