Question

A recent poll by the American Auto Club found that 40% of those surveyed are worried about aggressive drivers on the road. If 4 people are selected at random, what is the probability that all 4 will be worried about aggressive drivers on the road?

Answer 1

Probability that all 4 will be worried about aggressive drivers on the road is 0.0256.

Step-by-step explanation:

We are given that a recent poll by the American Auto Club found that 40% of those surveyed are worried about aggressive drivers on the road.  

Also, 4 people are selected at random.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 4 people

            r = number of success = all 4

           p = probability of success which in our question is % of those

                 surveyed are worried about aggressive drivers, i.e; 40%

LET X = Number of people who are worried about aggressive drivers

So, it means X ~ Binom(n = 4, p = 0.40)

Now, probability that all 4 will be worried about aggressive drivers on the road is given by = P(X = 4)

                   P(X = 4)  =  $\binom{4}{4}\times 0.40^{4} \times (1-0.40)^{4-4}$

                                  =  $1\times 0.40^{4} \times 0.60^{0}$

                                  =  0.0256

Hence, the probability that all 4 will be worried about aggressive drivers on the road is 0.0256.

Learn more about binomial distribution questions;

https://brainly.com/question/15719320