Question

According to a survey, 60% of people have a dog. If 5 people are selected randomly, what is the probability that at least 2 of them have a dog? Round the answer to the nearest tenth of the percent

Answer 1

Answer:

The probability is 18.7%

Step-by-step explanation:

The probability of owing a dog is 60% = 6/10

The probability of not owning a dog = 1-probability of owning a dog = 1-6/10 = 4/10

Now, out of five people, we need the probability that at least 2 own a dog.

That is probability that 2, 3, , 4 or even 5 owns a dog

If 2 owns, 3 doesn’t own

The probability here would be;

6/10 * 6/10 * 4/10 * 4/10 * 4/10 = 2,304/100,000

If three owns, this means 2 doesn’t own

The probability here would be

6/10 * 6/10 * 6/10 * 4/10 * 4/10 = 3,456/100,00

If 4 owns, 1 doesn’t own

Probability here is;

6/10 * 6/10 * 6/10 * 6/10 * 4/10 = 5,184/100,000

Lastly if 5 owns, we have

6/10 * 6/10 * 6/10 * 6/10 * 6/10 = 7,776/100,000

The total probability here is thus;

(7776 + 5,184 + 3,456 + 2,304)/100,000 = 18,720/100,000 = 0.1872 or simply 18.72%

To the neatest tenth of a percent, we have 18.7%