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

daniel 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|6|\n|suede|7|7|\n|silk|10|7|\nwhat is the probability that a randomly selected bow tie is made of silk given that the bow tie is shaped like a butterfly?\nsimplify any fractions.

daniel 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|6|\n|suede|7|7|\n|silk|10|7|\nwhat is the probability that a randomly selected bow tie is made of silk given that the bow tie is shaped like a butterfly?\nsimplify any fractions.

Answer

Explanation:

Step1: Identify relevant values

We want P(Silk|Butterfly). Number of silk - butterfly ties is 10, number of butterfly - shaped ties is (5 + 7+10=22).

Step2: Apply conditional - probability formula

The formula for conditional probability (P(A|B)=\frac{P(A\cap B)}{P(B)}). In terms of counts, (P(\text{Silk}|\text{Butterfly})=\frac{\text{Number of silk and butterfly ties}}{\text{Number of butterfly - shaped ties}}). So (P(\text{Silk}|\text{Butterfly})=\frac{10}{22}).

Step3: Simplify the fraction

(\frac{10}{22}=\frac{5}{11}).

Answer:

(\frac{5}{11})