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

bryant 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 | 4 | 3 |\n| grape jelly | 3 | 3 |\nwhat is the probability that a randomly selected sandwich was made with grape jelly given that the sandwich was made with creamy peanut butter?\nsimplify any fractions.

bryant 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 | 4 | 3 |\n| grape jelly | 3 | 3 |\nwhat is the probability that a randomly selected sandwich was made with grape jelly given that the sandwich was made with creamy peanut butter?\nsimplify any fractions.

Answer

Explanation:

Step1: Find total creamy peanut butter sandwiches

Add the number of creamy peanut - butter sandwiches with strawberry jelly and grape jelly. $4 + 3=7$.

Step2: Find number of creamy peanut butter and grape jelly sandwiches

The number of creamy peanut - butter and grape jelly sandwiches 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 grape jelly and $B$ is the event of having creamy peanut butter, the probability is the number of sandwiches with both grape jelly and creamy peanut butter divided by the number of sandwiches with creamy peanut butter. So the probability is $\frac{3}{7}$.

Answer:

$\frac{3}{7}$