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Answer:
Step-by-step 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:
We can find also the probaility that pedestrian was intoxicated AND driver was intoxicated, like this:
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:
And since w ehave everything to replace we got: