Employment data at a large company reveal that 59 % of the workers are married, that 43 % are college graduates, and that 1/3 of the college graduates are married. What is the probability that a randomly chosen worker is: a) neither married nor a college graduate? Answer = % b) married but not a college graduate? Answer = % c) married or a college graduate?

a. 74.63%

b. 33.63%

c. 87.67%

Step-by-step explanation:

If 59% (0.59) of the workers are married, then It means (100-59 = 41%) of the workers are not married.

If 43% (0.43) of the workers are College graduates, then it means (100-43 = 57%) of the workers are not college graduates.

If 1/3 of college graduates are married, it means portion of graduate that are married = 1/3 * 43% = 1/3 * 0.43 = 0.1433.

For question a, Probability that the worker is neither married nor a college graduate becomes:

= (probability of not married) + (probability of not a graduate) - (probability of not married * not a graduate)

= 0.41 + 0.57 - (0.41*0.57) = 0.98 - 0.2337

= 0.7463 = 74.63%

For question b, probability that the worker is married but not a college graduate becomes:

= (probability of married) * (probability of not a graduate.)

= 0.59 * 0.57

= 0.3363 = 33.63%

For question c, probability that the worker is either married or a college graduate becomes:

=probability of marriage + probability of graduate - (probability of married and graduate)

= 0.59 + 0.43 - (0.1433)

= 0.8767. = 87.67%