Question

Suppose that 38% of people own dogs. If you pick two people at random, what is the probability that they both own a dog? Give your answer as a decimal (to at least 3 places) or fraction

Answer 1

We are given that 38% of the people own dogs, thus if we choose a random person, the probability that he/she owns a dog is 38% or 0.38.

Now, we pick two people at random from the population and we are asked to calculate the probability that they both own dogs.

First we observe that :

P(Both the people own dogs) = P(first person own dogs)*P(second person own dogs)

because we can conveniently assume that "owning dogs" is independent between the two people.

Now, the two probabilities on the right hand side of the above equation, both equal 0.38 since the probability of a random person owning dogs is 0.38. Thus :

P(Both the people own dogs) = 0.38*0.38 = 0.1444 = 14.44%

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