Question

Do you tailgate the car in front of you? About 35% of all drivers will tailgate before passing, thinking they can make the car in front of them go faster. Suppose that you are driving a considerable distance on a two-lane highway and are passed by 6 vehicles.

a) Compute the expected number of vehicles out of 6 that will tailgate.

Answer 1

The expected number of vehicles out of 6 that will tailgate is 2.1.

Step-by-step explanation:

To compute the expected number of vehicles out of 6 that will tailgate, we can use the probability of tailgating which is given as 35% or 0.35. Since the passing of each vehicle is independent, the expected number of vehicles tailgating can be calculated by multiplying the total number of vehicles (6) by the probability of tailgating (0.35). Therefore, the expected number of vehicles out of 6 that will tailgate is 6 * 0.35 = 2.1.

Answer 2

To calculate the expected number of vehicles that will tailgate out of the 6 that pass, multiply the number of vehicles by the probability of tailgating (0.35). The expected value is 2.1 vehicles.

Step-by-step explanation:

To compute the expected number of vehicles that will tailgate out of the 6 vehicles that pass, we use the concept of expectation in probability. Since 35% of all drivers tailgate before passing, we can express this as a probability of 0.35. The expected value is calculated by multiplying the probability of an event by the number of trials, in this case, the number of vehicles.

The formula to compute the expected value (EV) is:

EV = n × p

Where n is the number of vehicles that pass by (6 in this example), and p is the probability of a driver tailgating (0.35).

So, the calculation will be as follows:

EV = 6 × 0.35 = 2.1

Therefore, the expected number of vehicles that will tailgate out of the 6 that will pass is 2.1.