Question

students who work at a local coffee shop recorded the drink orders of all the customers on a saturday. they found that 64% of customers ordered a hot drink, and 80% of these customers added cream to their drink. find the probability that a randomly selected saturday customer ordered a hot drink and added cream to the drink. probability = (round to 3 decimal places. leave your answer in decimal form.)

Explanation:

Step1: Calculate the combined probability

We use the multiplication rule for independent events. If \(A\) is the event that a customer ordered a hot drink (\(P(A)=0.64\)) and \(B\) is the event that a customer added cream given they ordered a hot drink (\(P(B|A) = 0.8\)). The formula for the probability of \(A\) and \(B\) is \(P(A\cap B)=P(A)\times P(B|A)\).

$$P = 0.64\times0.8$$

Step2: Perform the multiplication

$$0.64\times0.8=(64\times8)\times10^{- 3}=512\times10^{-3}=0.512$$

Answer:

\(0.512\)