Posted by Cece on Sunday, November 10, 2013 at 12:44am.
1. A customer comes into Pierre's and orders a random assortment of 6 danish. At the time she comes in, there are 26 danish sitting out: 12 raspberry, 8 cheese, and 6 cinnamon. Assume the danish are not replaced.
a) 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?
b) What is the probability that the random assortment will contain at least 1 cheese danish?
2. At Pierre's Coffee Shop, 57% of customers order coffee, 24% order tea and 16% order orange juice, while 3% do not order anything to drink. In addition, 43% order a muffin, 34% order a danish and 14% order a bagel, while 9% do not order anything to eat. Finally, 26% of customers order both coffee and a danish, and 47% of people order a bagel given that they have ordered tea. Assume that an individual customer will not order more than once drink or more than one breakfast roll.
a) When the coffee shop opens, what is the probability that the first person to not order anything to eat is the fifth person to enter the shop?
b) What is the probability that a particular customer will order coffee given that he did NOT order a danish?

Math  Reiny, Sunday, November 10, 2013 at 11:05am
I will do #1
#1
let R represent picking a raspberry, N a nonraspberry
12R , 14N
a) so you want: NNRNRN
prob = (14/26)(13/25)(12/24)(12/23)(11/22)(11/21)
= .01913
Prob(none cheese)= (18*17*16*15*14*13)/(26*25*24*23*22*21)
= .08063
at least one cheese
= 1  .08063
= .91936