Question

Eighty percent of all California drivers wear seat belts. If three drivers are pulled over,

what is the probability that all would be wearing their seat belts? Write as a percent to the nearest tenth. Thanks!

Answer 1

The probability that the three drivers would wear seat belts is 0.5

Explanation:

Given

Percentage of drivers using seat belt = 80%

Number of drivers pulled over = 3

Required

Probability that all three drivers wore seat belt

First, the probability that a driver would wear seat belt has to be calculated.

Let's represent that with P(D)

P(D) is equivalent to the percentage of drivers using seat belt

`P(D) = 80%`%

`P(D) = (80)/(100)`

`P(D) = 0.8`

Let the probability that the three drivers would wear seat belts be represented as P(All).

P(All) is calculated as thus;

(Probability that the first driver would wear seat belt) and (Probability that the second driver would wear seat belt) and (Probability that the first driver would wear seat belt).

Mathematically, this means

`P(All) = P(D) * P(D) * P(D)`

Substitute
`P(D) = 0.8`

`P(All) = 0.8 * 0.8 * 0.8`

`P(All) = 0.512`

`P(All) = 0.5` --- Approximated

Hence, the probability that the three drivers would wear seat belts is 0.5