Question

Suppose that 25% of people own dogs If you pick three people at random, what

is the probability that they all three own a dog? (Let me add that we don’t know the
populations size so calculate the probability as if the population is infinite.)

Answer 1

1/64

Explanation:

25% own a dog, so picking one person has a probability of 1/4 (0.25) for that person to own a dog.

picking 3 people means combining (multiplying) the probabilities of the non-overlapping and non-depending events.

picking the third person has 1/4 chance of owning a dog (as the population is "infinite") combined with the chance that also the second pick owned a dog, which has to be combined with the chance of the first pick owning a dog.

so,

1/4 × 1/4 × 1/4 = 1/4³ = 1/64 = 0.015625