Question

brett is a sandwich maker at a local deli. last week, he tracked the number of peanut butter and jelly sandwiches ordered, noting the flavor of jelly and type of peanut butter requested.

	creamy peanut butter	chunky peanut butter
grape jelly	8	3
orange jelly	2	3

what is the probability that a randomly selected sandwich was not made with orange jelly and was not made with creamy peanut butter?
simplify any fractions.

Explanation:

Step1: Calculate total number of sandwiches

Add all the values in the table: \(7 + 6+8 + 3+2 + 3=\sum_{i = 1}^{6}x_{i}=29\)

Step2: Find number of sandwiches that meet the criteria

Sandwiches that are not orange jelly and not creamy peanut - butter are strawberry jelly with chunky peanut butter (\(6\)) and grape jelly with chunky peanut butter (\(3\)). So \(6 + 3=9\)

Step3: Calculate the probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{9}{29}\)

Answer:

\(\frac{9}{29}\)