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.\n| |creamy peanut butter|chunky peanut butter|\n|--|--|--|\n|strawberry jelly|3|3|\n|grape jelly|3|6|\nwhat is the probability that a randomly selected sandwich was made with creamy peanut butter given that the sandwich was made with grape jelly?\nsimplify 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.\n| |creamy peanut butter|chunky peanut butter|\n|--|--|--|\n|strawberry jelly|3|3|\n|grape jelly|3|6|\nwhat is the probability that a randomly selected sandwich was made with creamy peanut butter given that the sandwich was made with grape jelly?\nsimplify any fractions.

Answer

Explanation:

Step1: Calculate total grape - jelly sandwiches

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

Step2: Calculate number of grape - jelly and creamy peanut - butter sandwiches

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

Step3: Use conditional probability formula

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 $P(A|B)=\frac{\text{Number of }A\cap B}{\text{Number of }B}$. So the probability is $\frac{3}{9}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$