Education Level and Smoking At a large factory, the employees were surveyed and classified according to their level of education and whether they smoked. The data are shown in the table.

If an employee is selected at random, find these probabilities.

a. The employee smokes, given that he or she graduated from college.

b. Given that the employee did not graduate from high school, he or she is a smoker. (4–3)

Step 1:

The data about the employees who are classified according to their level of education and whether they smoked is given.

Educational level |
||||

Smoking habit |
Not high school graduate |
High school graduate |
College graduate |
Total |

Smoke |
6 |
14 |
19 |
39 |

Do not smoke |
18 |
7 |
25 |
50 |

Total |
24 |
21 |
44 |
89 |

An employee is selected randomly.

We have to find the following probabilities.

The employee smokes, given that he or she graduated from college.He or she is a smoker, given that the employee did not graduate from high school.Step 2:

By the classical definition of probability,

Probability = .

And by the definition of conditional probability,

P (A/B) =

(a)

The probability that the employee smokes, given that he or she graduated from college.

P (that the employee smokes/ graduated from college) =

P (that employee smokes graduated from the college) =

P (graduated from the college) =

P (that the employee smokes/ graduated from college) =

=

= 0.4318

Therefore, the probability that the employee smokes, given that he or she graduated from college is 0.4318.