rudy is a sandwich maker at a local deli. last week, he tracked the number of peanut butter and jelly…

rudy 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. what is the probability that a randomly selected sandwich was made with creamy peanut butter given that the sandwich was made with grape jelly? simplify any fractions.

rudy 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. what is the probability that a randomly selected sandwich was made with creamy peanut butter given that the sandwich was made with grape jelly? simplify any fractions.

Answer

Explanation:

Step1: Find number of grape - jelly sandwiches

The number of grape - jelly sandwiches is the sum of those with creamy and chunky peanut butter. So, $3 + 6=9$.

Step2: Find number of grape - jelly sandwiches with creamy peanut butter

The number of grape - jelly sandwiches with creamy peanut butter is 3.

Step3: Calculate conditional probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if $A$ is the event of having creamy peanut butter and $B$ is the event of having grape jelly, then the probability that a sandwich has creamy peanut butter given it has grape jelly is $\frac{\text{Number of grape - jelly and creamy peanut butter sandwiches}}{\text{Number of grape - jelly sandwiches}}=\frac{3}{9}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$