myra designs bow ties for a local boutique store. the store manager counted the ties currently on display…

myra designs bow ties for a local boutique store. the store manager counted the ties currently on display, tracking them by material and shape.\n| |butterfly|batwing|\n|--|--|--|\n|cotton|5|2|\n|suede|4|5|\nwhat is the probability that a randomly selected bow tie is made of suede given that the bow tie is shaped like a batwing?\nsimplify any fractions.

myra designs bow ties for a local boutique store. the store manager counted the ties currently on display, tracking them by material and shape.\n| |butterfly|batwing|\n|--|--|--|\n|cotton|5|2|\n|suede|4|5|\nwhat is the probability that a randomly selected bow tie is made of suede given that the bow tie is shaped like a batwing?\nsimplify any fractions.

Answer

Explanation:

Step1: Find number of batwing - shaped ties

The number of batwing - shaped ties is the sum of cotton and suede batwing - shaped ties. So, $2 + 5=7$.

Step2: Find number of suede batwing - shaped ties

The number of suede batwing - shaped ties is 5.

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 that the tie is suede and $B$ is the event that the tie is batwing - shaped, then $P(A|B)=\frac{\text{Number of suede and batwing - shaped ties}}{\text{Number of batwing - shaped ties}}$. So the probability is $\frac{5}{7}$.

Answer:

$\frac{5}{7}$