Question

At a local animal shelter, 62% of puppies get adopted and 71% live to be at least 7 years old. 46% of the puppies are both adopted and live to be at least 7 years old. What isthe probability that a randomly selected puppy in the shelter will get adopted or live 7 or more years?

Answer 1

Given the information

62% get adopted

71% live at least 7 years

46% are both, adopted and live 7 years

Prob adopted or live 7 or more years = ?

since

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

where

P(AuB)= Prob adopted or live 7 or more years =?

P(A)= 62% get adopted

P(B)= 71% live at least 7 years

P(AnB)=46% are both, adopted and live 7 years

$P(A\cup B)=62\%+71\%-46\%$$P(A\cup B)=87\%$

the probability that a randomly selected puppy in the shelter will get adopted or live 7 or more years is 87%

as an exact decimal

0.87