4. One morning a customer comes into Pierre\'s and orders a random assortment of

Question

4. One morning a customer comes into Pierre's and orders a random assortment of 6 danish. At the time she comes in, there are 27 danish sitting out: 11 raspberry, 9 cheese, and 7 cinnamon. Assume the danish are not replaced after they are selected. What is the probability that the third and fifth danish selected for the customer's random assortment will be raspberry, and the other four will not be raspberry? (5 pts) Suppose that 24% of the people that come into Pierre's order a double chocolate mochaccino, while 76% do not. Assume that each person is independent of the any other. 5. Suppose seven people show up at the coffee shop at the same time. What is the probability that exactly four of them will order the mochaccino? (4 pts) a)

Explanation / Answer

(4)

Sol:Let R represent picking a raspberry,N is a non raspberry
11R,16N
So you want NNRNRN
Probability=(16/27)(15/26)(11/25)(14/24)(10/23)(13/23)
                =0.02156
the probability that the third and fifth danish selected for the customer's random assortment will be raspberry and the other four will not be raspberry

(5)

Sol:Given p=0.24

               q=0.76

              n=7

P(x=4)=7c4(0.24)4(0.76)7-4

          =35*0.0033*0.4389

          =0.0509

the probability that exactly 4 of them will order the mochaccino is 0.0509

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