It has been determined that only 80 of the people wear seat

It has been determined that only 80% of the people wear seat belts. If a police officer stops a car with four people, what is the probability that at least one person will not be wearing a seat belt?

Solution

Probability of wearing a seat belt = 0.80
probabiltiy of not wearing = 0.20

Probability of at one person not wearing a seat belt = 1 - P( all wearing seast belt)

                                                                         = 1- 4C₄ (0.80)⁴

                                                                                                = 1- 0.4096   = 0.5904 (ans)