Question

The following data summarizes results from 889 pedestrian deaths that were caused by accidents. If one of the pedestrian deaths is randomly​ selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated. Pedestrian intoxicated Driver intoxicated 50 91Pedestrian not intoxicated Driver not intoxicated 209 539P (pedestrian was intoxicated or driver was ​intoxicated) = ________?

Answer 1

`P(A or B) = 0.291 +0.159 -0.0562=0.3938`

Explanation:

Previous concepts

The total probability rule is "used to find the probability of an event, A, when you don’t know enough about A’s probabilities to calculate it directly. Instead, you take a related event, B, and use that to calculate the probability for A".

Solution to the problem

The data given:

Pedestrian

Intoxicated Not intoxicated Total

Intoxicated 50 91 141

Not intoxicated 209 539 748

Total 259 630 889

The rows on this case are associated to the tyep of Driver.

Let's define the following events:

A =Pedestrian was intoxicated

B= Driver was intoxicated

And we can find the probabilities for the events A and B like this with the info given:

`P(A) = (50+209)/(889)=0.291`

`P(B) = (50+91)/(889)=0.159`

We can find also the probaility that pedestrian was intoxicated AND driver was ​intoxicated, like this:

`P(A and B) = (50)/(889)=0.0562`

Because the intersection for the events A and B is 50 and the grand total is 889.

Now we can use the total rule of probability given by this:

`P(A or B) = P(A) +P(B) -P(A and B)`

And since w ehave everything to replace we got:

`P(A or B) = 0.291 +0.159 -0.0562=0.3938`