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

antonio 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|1|4|\n|suede|4|6|\nwhat is the probability that a randomly selected bow tie is made of suede given that the bow tie is shaped like a butterfly?\nsimplify any fractions.

antonio 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|1|4|\n|suede|4|6|\nwhat is the probability that a randomly selected bow tie is made of suede given that the bow tie is shaped like a butterfly?\nsimplify any fractions.

Answer

Explanation:

Step1: Identify relevant numbers

Number of butterfly - shaped suede ties = 4, number of butterfly - shaped ties = 1 + 4 = 5.

Step2: Apply 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 the tie being suede and $B$ is the event of the tie being butterfly - shaped, then $P(A|B)=\frac{\text{Number of suede and butterfly - shaped ties}}{\text{Number of butterfly - shaped ties}}$. So the probability is $\frac{4}{1 + 4}$.

Answer:

$\frac{4}{5}$