A food truck sells three kinds of tacos: beef, chicken and bean. Half of custome

Question

A food truck sells three kinds of tacos: beef, chicken and bean. Half of customers buy beef tacos. Customers are twice as likely to buy chicken tacos as they are to buy bean tacos. For simplicity, assume that each customer buys exactly one kind of tacos What is the probability that a randomly selected customer buys bean tacos? What is the probability that a randomly selected customer buys beef tacos or bean tacos? What is the probability that a randomly selected customer buys beef tacos and bean tacos?

Explanation / Answer

let A be the event that a customer buys beef tacos.

B be the event that a customer buys chicken tacos

C be the event that a customer buys bean tacos.

Half of customers buy beef tacos. Customers are twice as likely to buy chicken tacos as they are to buy bean tacos.

so P[A]=0.5   

let P[C]=x then P[B]=2x.

so 0.5+2x+x=1   [as the assumption is that that each customer buys exactly one kind of tacos]

or, 3x=0.5 or x=1/6

so P[A]=1/2   P[B]=2/6=1/3   P[C]=1/6

so the probability that a randomly selected customer buys bean tacos=P[C]=1/6 [answer]

the probability that a randomly selected customer buys beef tacos or bean tacos is

P[A]+P[C]=1/2+1/6=2/3

the probability that a randomly selected customer buys beef tacos and bean tacos is zero [since the assumption is each customer buys exactly one kind of tacos]     [answer]

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