Question

: Two hundred students were randomly selected and surveyed at a small central Ohio university. They were asked about driving while intoxicated over their four week winter/holiday break. The results are summarized in the table below. (2 points each)

	Did you have a driving accident?
	Yes	No	Total
Intoxicated	16	8	24
Sober	3	173	176
Total	19	181	200

1.     What is the probability of encountering a student who said they were intoxicated when they were driving during the winter/holiday break?   

  

2.     What is the probability of encountering a student who said they had an accident during the winter/holiday break?  

3.     What is the probability of encountering a student who said they had been intoxicated and had an accident during the winter/holiday break?    

4.     What is the probability of encountering a student who said they did not have and accident and had been sober during the winter/holiday break?   

5.     What is the probability of encountering a student who said they did not have an accident given that they were sober during the winter/holiday break?   

6.     What is the probability of encountering a student who had an accident given that they were sober?       

7.     Are the events “having a driving accident” and “being sober” mutually exclusive events? Why?

Be sure Numbers and Equations are correct.

9.   Are the events “having a driving accident” and “being sober” independent events? Why?

Answer 1

1) There are 24 students who were intoxicated when they were driving during the winter/holiday break. Hence the probability is

2) There are 19 students who said they had an accident during the winter/holiday break. hence the probability is

3) There are 16 students who said they had been intoxicated and had an accident during the winter/holiday break

So the probability is

4) There are 173 students who said they did not have and accident and had been sober during the winter/holiday break so the probability is

5) There are 176 students who are Sober and among them 173 did not have an accident

Hence the probability is

6) There are 176 students who are Sober and among them, 3 did have an accident

Hence the probability is

7) Since Mutually Exclusive can't happen at the same time. So the events “having a driving accident” and “being sober” are not mutually exclusive events.

8) There are 3 students who said they had an accident and had been sober during the winter/holiday break.

Also, 19 have an accident and 176 are Sober

Since

So the the events “having a driving accident” and “being sober” are not independent events