At Chuck\'s BYO (Build Your Own) Ice Cream Sunday Bar, you have the following ch

Question

At Chuck's BYO (Build Your Own) Ice Cream Sunday Bar, you have the following chooses: Ice Cream: Vanilla (V), Chocolate (C) , Strawberry (S) Toppings: Oreos (O), M&Ms (M), Reeses (R) a) If a customer must choose exactly 1 ice cream and 1 topping and they choose each at random (uniformly), what is the probability that a customer has strawberry ice cream with Oreos on top? In other words, determine P {SO} . State any assumptions you have made to get this answer (there is at least one assumption that must be made) and show your work. b) Let the probabilities that a customer orders a given topping be: P{O} = 0.2, P{M} = 0.3 and P{R} = 0.5. In addition, Chuck has also determined that if a customer chooses to have Reeses as their topping, they also select Vanilla ice cream (i.e., P{V | R}) with probability 0.5, Chocolate (i.e., P{C | R}) with probability 0.2, and strawberry (i.e., P{S | R}) with probability 0.3. If the customer chooses M&Ms as a topping, they select Vanilla, Chocolate, and strawberry ice creams with probabilities 0.1, 0.6, and 0.3, respectively. Finally, if the customer selects Oreos as their topping, they select Vanilla, Chocolate, and strawberry ice creams with probabilities 0.4, 0.2, and 0.4, respectively. Determine the probability that a customer order vanilla ice cream (i.e, P{V}). . c) Use the result and probabilities given in part b) to determine P{R | V}: i.e., the probability that a person gets Reeses topping given that they got Vanilla ice cream. If you could not solve part b), assume here that P{V} = 0.6.

Explanation / Answer

Assumption is selection of type of ice cream and selection of topping are independent.

The probability that a customer has strawberry ice cream with Oreos on top, In other words,

P {SO} = P(S)*P(O) = (1/3) * (1/3) = 1/9

b) Let the probabilities that a customer orders a given topping be: P{O} = 0.2, P{M} = 0.3 and P{R} = 0.5. P{V | R}=0.5, P{C | R} =0.2, P{S | R} = 0.3.; P(V|M) = 0.1; P(C|M)=0.6 ; P(S|M) =0.3; P(V|O) =0.4; P(C|O)=0.2 ; P(S|O) = 0.4

Determine the probability that a customer order vanilla ice cream (i.e, P{V}). .

P(V) = P(O) * P(V|O) + P(M) * P(V|M) + P(R) *P(V|R) = 0.2*0.4 + 0.3*0.1 + 0.5*0.5 =0.36

C) P(R|V) = P(R and V) /P(V) = P(R)*P(V|R) / P(R) = (0.5*0.5)/0.36 = 0.69444

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.