According to the u. s. bureau of labor statistics, 75% of the women 25 through 49 years of age participate in the labor force. suppose 78% of the women in that age group are married. suppose also that 61% of women 25 through 49 years of age are married and are participating in the labor force. (round your answers to 2 decimal places.)a. what is the probability that a randomly selected woman in that age group is married or is participating in the labor force? p = . what is the probability that a randomly selected woman in that age group is married or is participating in the labor force but not both? p = . what is the probability that a randomly selected woman in that age group is neither married nor participating in the labor force? p =

a) There is a 92% probability that a randomly selected woman in that age group is married or is participating in the labor force.

b) There is a 31% probability that a randomly selected woman in that age group is married or is participating in the labor force but not both.

c) This means that there is an 8% probability that a randomly selected woman in that age group is neither married nor participating in the labor force.

Step-by-step explanation:

We can solve this problem building the Venn's diagram of these probabilities.

I am going to say that

The set A are those women who participate in the work force.

The set B are those women who are married.

We have that:

In which a represents those that participate in the work force but are not married and are those who are both on the work force and married.

By the same logic, we have that:

We start finding the values from the intersection of these sets:

Suppose also that 61% of women 25 through 49 years of age are married and are participating in the labor force.

This means that

Suppose 78% of the women in that age group are married.

This means that

75% of the women 25 through 49 years of age participate in the labor force.

This means that

a. What is the probability that a randomly selected woman in that age group is married or is participating in the labor force

This is

There is a 92% probability that a randomly selected woman in that age group is married or is participating in the labor force.

b. What is the probability that a randomly selected woman in that age group is married or is participating in the labor force but not both?

This is

There is a 31% probability that a randomly selected woman in that age group is married or is participating in the labor force but not both.

c. What is the probability that a randomly selected woman in that age group is neither married nor participating in the labor force?

From a), we found that there is a 92% probability that a randomly selected woman in that age group is married or is participating in the labor force.

This means that there is an 8% probability that a randomly selected woman in that age group is neither married nor participating in the labor force.

the answer is c

step-by-step explanation: