If a household has at least one cat there is a 30 probabilit

If a household has at least one cat, there is a 30% probability that the household has at least one dog. Thirty percent of households have at least one cat and 33% of households have at least one dog. Given that a household has at least one dog, the probability that the same household has at least one cat is ________.

0.06

0.17

0.27

0.48

Solution

Let

D = at least one dog
C = at least one cat

Hence, it is given that

P(D|C) = 0.30
P(C) = 0.30
P(D) = 0.33

Thus,

P(C|D) = P(C) P(D|C) / P(D) = 0.30*0.30/0.33 = 0.272727273 = 0.27 [ANSWER, C]