Problema Solution

A kennel has 400 dogs. There are 200 poodles and 150 dogs with with shaggy hair. If 12.5% of the poodles have shaggy hair, what is the probability that one randomly selected dog will be a poodle or will have shaggy hair?

Answer provided by our tutors

A: the selected dog is a poodle


B: the selected dog has shaggy hair


P(A or B) = P(A) + P(B) − P(A and B)


P(A) = 200/400


P(A) = 1/2


P(B) = (0.125*200 + 150)/400


P(B) = 7/16


P(A and B) = 0.125*200/400


P(A and B) = 1/16


P(A or B) = 1/2 + 7/16 − 1/16


P(A or B) = 7/8


P(A or B) = 0.875


The probability that one randomly selected dog will be a poodle or will have shaggy hair is 0.875.