2. In a certain convenience store, there are three different brands of soda Cake

Question

2. In a certain convenience store, there are three different brands of soda Cake, Peps, and Sprite in stock. On any Oven day, you can expect that of all the soda n stock, 40% is Coke, 35%is Pepsi, and the remaining 2S is Spre When looking at the stock of each particular brand, the portion that is diet soda breaks down as such 0.5 of the Coke products are diet, 0.4 of Pepsi products are diet, and 0 2 of Sprite products are diet a) What is the probability that a random customer purchasing a soda buys a diet soda? random customer in the store is observed to have bought a diet soda, what is the probability that the soda b) If a brand is Coke?

Explanation / Answer

Ans:

Given that

P(coke)=0.40

P(pepsi)=0.35

P(sprite)=0.25

Also,

P(diet/coke)=0.5

P(diet/ pepsi)=0.4

P(diet/sprite)=0.2

a)

P(diet)=P(diet/coke)*P(coke)+P(diet/pepsi)*P(pepsi)+P(diet/sprite)*P(sprite)

=0.5*0.40+0.4*0.35+0.2*0.25

=0.20+0.14+0.05

=0.39

b)

P(coke/diet)=P(diet/coke)*P(coke)/P(diet)=0.5*0.40/0.39=0.5128

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