Question

According to government data, about 78% of U.S. households have an automatic dishwasher. If 15 households are selected at random, what is the probability that 9 of them have an automatic dishwasher? Enter your answer using three decimal places.

Answer 1

We compute the probability using binomial law like this:

`C_(15)^90.78^9(1-0.78)^6=(15!)/(9!(15-9)!)0.78^9(1-0.78)^6\\\approx0.06\text{ (use a calculator in order to evaluate the expression )}`

Answer 2

Answer: 0.061

Explanation:

Given : The probability of U.S. households have an automatic dishwasher. : p=0.78

Sample size : n=15

Using binomial distribution, we have

`P(x)=^nC_xp^x(1-p)^(n-x)` , where P(x) is the probability of getting success in x trials , p is the probability of getting success in each trial.

Now, the the probability that 9 of them have an automatic dishwasher will be :_

`P(9)=^(15)C_9(0.78)^9(1-0.78)^(15-9)\\\\=(15!)/(9!(15-9)!)*(0.78)^9(0.22)^6\\\\=0.0606445239086\approx0.061`

Hence, the probability that 9 of them have an automatic dishwasher = 0.061