Question

Charlie designs bow ties for a local boutique store. The store manager counted the ties currently on display, tracking them by material and shape. Cotton Suede 4 8 Butterfly Batwing 5 3 What is the probability that a randomly selected bow tie is shaped like a batwing or is made of cotton Simplify any fractions.

Answer 1

The grand total n is given by

`n=4+8+5+3=20`

The marginal probability for a batwing shape is given by

`P(\text{batwing)}=(5)/(20)+(3)/(20)=(8)/(20)`

and the marginal probability for Cotton is

`P(\text{cotton)}=(4)/(20)+(5)/(20)=(9)/(20)`

Then, the probability that a bow tie is shaped like a batwing or is made of cotton is given by

`P(batwingU\cot ton)=P(\text{batwing)}+P(\text{cotton)}=(8)/(20)+(9)/(20)=(17)/(20)`

so, the answer is 17/20