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At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. What is the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item?

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Answer:

0.196

Step-by-step explanation:

Let :

Expresso drink = A

Plain coffee = B

Food = F

P(A) = 0.56

P(B) = 0.44

P(F) = 0.40

P(F|A) = 0.35

P(F|B) = 0.30

Probability that a customer purchases a specialty expresso coffee and a food item :

P(F|A) =. P(F n A) / P(A)

P(F n A) = P(F|A) * P(A)

P(F n A) = 0.35 * 0.56

P(F n A) = 0.196

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