Question

Seat belt use in a state was estimated at ​%, which means ​% of people use their seat belts. Suppose two independent drivers have been randomly selected. a. What is the probability that both of them are using a​ seatbelt? b. What is the probability that neither of them is using a​ seatbelt? c. What is the probability that at least one is using a​ seatbelt? a. The probability that both of them are using a seatbelt is 0.3. ​(Type an integer or a decimal. Do not​ round.)

Answer 1

Question

Seat belt use in a state was estimated at 89%,

which means 89 % of people use their seat belts. Suppose two independent drivers have been randomly selected.

a. What is the probability that both of them are using a​seatbelt?

b. What is the probability that neither of them is using a​seatbelt?

c. What is the probability that at least one is using a​seatbelt?

The probability that both of them are using a seatbelt is ?

Answer:

a

$P(B) = 0.7921$

b

$P(B)' = 0.0121$

c

$P(K) = 0.9879$

Step-by-step explanation:

From the question we are told that

    The proportion of seat belt use is  p =  0.89

     The  sample  size n =  2

Generally the probability that both drivers are wearing seat belt is mathematically represented as

       $P(B) = (p)^n$

=>     $P(B) = (0.89 )^2$

=>     $P(B) = 0.7921$

Generally the probability that neither of the two drivers are wearing seat belt is  

      $P(B)' = (1 - p)^2$

=>   $P(B)' = (1 - 0.89)^2$

=>   $P(B)' = 0.0121$

Generally the probability that at least one of the drivers is wearing a seat belt is  

        $P(K) = 1 - P(B)'$

=>     $P(K) = 1 - 0.0121$

=>     $P(K) = 0.9879$