Question

A local food truck sells three items:

Chicken

Waffles

Slaw

Consider the next customer to be a randomly selected customer. The customer can order any one, two, or three items, but no duplicates!

This customer places an order that includes all three items with probability 0.23. His order includes Chicken or Waffles with probability 0.99, that includes Chicken or Slaw with probability 0.78, and that includes Waffles or Slaw with probability 0.90. His order includes Chicken with probability 0.75, includes Waffles with probability 0.84.

What is the probability that the customer's order is for Chicken and Waffles, without Slaw?

Answer 1

From the given information we have

P(all three) = 0.23

and

P(Chicken or Waffles) = 0.99, P(Chicken) = 0.75 and P(Waffles) = 0.84

From addition rule we have

P(Chicken and Waffles)= P(Waffles)+P(Chicken)-P(Chicken or Waffles) = 0.84 + 0.75 - 0.99 = 0.60

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Now the probability that the customer's order is for Chicken and Waffles, without Slaw is

P(Chicken and Waffles and not Slaw) = P(Chicken and Waffles) - P(all three) = 0.60 - 0.23 = 0.37

Hence, answer is 0.37.