Question

Suppose that 45% of people have dogs. If two people are randomly chosen, what is the probability that they both have a dog

Answer 1

`P(Dogs) = 0.2025`

Explanation:

Given

`Proportion, p = 45\%`

Required

Probability of two people having dog

First, we have to convert the given parameter to decimal

`p = (45)/(100)`

`p = 0.45`

Let P(Dogs) represent the required probability;

This is calculated as thus;

P(Dogs) = Probability of first person having a dog * Probability of second person having a dog

`P(Dogs) = p * p`

`P(Dogs) = 0.45 * 0.45`

`P(Dogs) = 0.45^2`

`P(Dogs) = 0.2025`

Hence, the probability of 2 people having a dog is
`P(Dogs) = 0.2025`