Question

Each employee at an upscale bakery has a particular set of skills that can be applied to each cake that is ordered. There is one particular t baker, who is going to be on vacation for the next 2 weeks. Cakes requiring this decorating technique are ordered with the following probability each week 1. that can only be done by1 Number of Cakes Requiring Special Techniques01 23 Probability 0.6 0.2 0.15 0.05 If a cake requiring this technique is ordered while the baker is on vacation, then the bakery cannot fill the order. What is the probability that the bakery will receive at least one order that they cannot fill while the baker is on vacation?

Please show all work and steps!

Answer 1

Let X denotes the number of cakes requiring special techniques in a week The probability distribution of ordered cakes for decorating is shown below: Number of Cakes Requiring Special Techniques Probability 1 0 2 3 0.6 0.2 0.15 0.05 It is required to find the probability that the bakery will receive at least one order that they cannot fill while the baker is on vacation This implies, P(X21)1-P(X<1) =1-P(X 0) 1-0.6 0.4 Hence, the probability that the bakery will receive at least one order that they cannot fill while the baker is on vacation is 0.4