Question

question 3 (multiple choice worth 4 points) (h1 04h mc2) a diner has collected data about customer coffee - drinking habits. they have calculated that p(cream) = 0.5, p(sugar) = 0.6, and p(cream or sugar) = 0.7. determine the p(cream and sugar). options: 0.4, 0.5, 0.6, 0.7

Explanation:

Step1: Recall the addition rule for probability

The formula for the probability of the union of two events \( A \) and \( B \) is \( P(A \cup B)=P(A)+P(B)-P(A \cap B) \). Let \( A \) be the event of using cream and \( B \) be the event of using sugar. So we have \( P(\text{cream or sugar}) = P(\text{cream})+P(\text{sugar})-P(\text{cream and sugar}) \).

Step2: Substitute the known values

We know that \( P(\text{cream}) = 0.5 \), \( P(\text{sugar}) = 0.6 \), and \( P(\text{cream or sugar}) = 0.7 \). Substituting these into the formula: \( 0.7=0.5 + 0.6-P(\text{cream and sugar}) \).

Step3: Solve for \( P(\text{cream and sugar}) \)

First, calculate \( 0.5 + 0.6=1.1 \). Then the equation becomes \( 0.7 = 1.1-P(\text{cream and sugar}) \). Rearranging to solve for \( P(\text{cream and sugar}) \), we get \( P(\text{cream and sugar})=1.1 - 0.7 = 0.4 \).

Answer:

\( 0.4 \) (corresponding to the option with value \( 0.4 \))