Question

an arena manager tallies the number of snack items (hot dogs, nachos, and popcorn) sold at each of three concession stands in the arena. what is the probability that a customer purchased popcorn, given that they purchased from stand b? 6.9% 13.4% 14.0% 49.5%

Explanation:

Step1: Recall conditional probability formula

The formula for conditional probability is \( P(A|B)=\frac{P(A\cap B)}{P(B)} \). In the context of the table, if \( A \) is the event of purchasing popcorn and \( B \) is the event of purchasing from stand \( B \), then \( P(A|B)=\frac{\text{Number of popcorn sold at stand B}}{\text{Total number of items sold at stand B}} \).

Step2: Identify values from the table

From the table, the number of popcorn sold at stand \( B \) is \( 52 \), and the total number of items sold at stand \( B \) is \( 389 \).

Step3: Calculate the probability

\( P=\frac{52}{389}\approx 0.134 \). To convert this to a percentage, we multiply by \( 100 \), so \( 0.134\times100 = 13.4\% \).

Answer:

13.4%