2. Every day a bakery makes40 chocolate cupcakes, 50 vanilla cupcakes, 30 carame

Question

2. Every day a bakery makes40 chocolate cupcakes, 50 vanilla cupcakes, 30 caramel cupcakes, and 20 fruit cupcakes. No cupcakes are available from the day before (so you have the same available cupcakes to start each day). You are the first customer at the bakery every day for 7 days, and you are given a random cupcake out of the display case. What is the probability on any 1 day that you get a fruit cupcake? (3) a. What is the probability that of the 7 cupcakes you buy, 3 are chocolate, 2 are vanilla, 0 are caramel and 2 are fruit cupcakes? (5) b. Which distribution do you use to model and solve this problem? (2) c.

Explanation / Answer

a) P( Atleast one fruit cupcake) = 1-P( No fruit cupcake) = 1-(120/140)^7=0.6600

b) Probability = 7! / [ 3! * 2! * 2! ] *(40/120)^3 *(50/120)^2 *(20/120)^2 = 0.0375

c) Multiple binomial distribution is used to model this problem.

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