Question

A survey of home owners in a neighborhood found that 25% owned a dog, 40% owned a cat, and 15% owned both a dog and a cat.

What is the probability that a random homeowner has a dog given they have a cat?

What is the probability that a random homeowner from this neighborhood owns a cat given they have a dog?

What is the probability that a random homeowner from this neighborhood has a dog but not a cat?

What is the probability that a random homeowner from this neighborhood owns a dog or a cat?

Answer 1

here let event of owning a dog and cat are represented by D and C

therefore P(D) =0.25

P(C) =0.40

P(C n D) =0.15

1)

probability that a random homeowner has a dog given they have a cat =P(D|C) =P(C n D)/P(C)

=0.15/0.40

=0.375

2)

probability that a random homeowner from this neighborhood owns a cat given they have a dog

=P(C|D) =P(C n D)/P(D)=0.15/0.25 =0.6

3) probability that a random homeowner from this neighborhood has a dog but not a cat

=P(D)-P(D n C) =0.25-0.15 =0.10

4)

probability that a random homeowner from this neighborhood owns a dog or a cat

=P(D u C) =P(D)+P(C)-P(D n C) =0.25+0.40-0.15 =0.50