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

$P(\text{batwing)}=\frac{5}{20}+\frac{3}{20}=\frac{8}{20}$

and the marginal probability for Cotton is

$P(\text{cotton)}=\frac{4}{20}+\frac{5}{20}=\frac{9}{20}$

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

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

so, the answer is 17/20