Question

on a large college campus, 84% of the students report drinking alcohol within the past month, 33% report using some type of tobacco product within the past month, and 86% report using at least one of these two substances during the past month. in an experiment, a student is randomly selected from the college. calculate the probability that the student both drunk alcohol and used tobacco in the past month.

Answer 1

Answer: 0.31

Explanation:

Let A denotes the event that the students report drinking alcohol and B denotes the students report using some type of tobacco product .

Given : P(A) =0.84 ; P(B)=0.33 and P(A∪B)=0.86

We know that
`P(A\cap B)=P(A)+P(B)-P(A\cup B)`

Then, the probability that the student both drunk alcohol and used tobacco in the past month is given by :-

`P(A\cap B)=0.84+0.33-0.86=0.31`

Hence, the probability that the student both drunk alcohol and used tobacco in the past month = 0.31