Question

A study conducted through the University of Wisconsin examined food and housing insecurity among college students. In the study, students from 2- and 4-year colleges were asked to classify themselves based on relationship status, which had 5 options. The probabilities for randomly selecting a student from a 4-year with a particular relationship status is listed in the table below.

Relationship Status Single In a relationship Married Divorced Widowed Probability 0.56 0.34 ? .01 .001

a. For the distribution above to be valid, what must be the probability of randomly selecting a married student from a 4-year college?

b. What is the probability of randomly selecting a student from a 4-year college who is in a relationship or married?

c. Two people are chosen at random. What is the probability that both are single?

d. Two people are chosen at random. What is the probability that the first is “single” and the second is “in a relationship”?

e. Two people are chosen at random. What is the probability that at least one person is single

Answer 1

a)probability of randomly selecting a married student from a 4-year college =1-0.56-0.34-0.01-0.001=0.089

b) e probability of randomly selecting a student from a 4-year college who is in a relationship or married

=0.34+0.089=0.429

c) probability that both are single =0.56*0.56 =0.3136

d) probability that the first is “single” and the second is “in a relationship =0.56*0.34 =0.1904

e) probability that at least one person is single =1-P(none is single)=1-(1-0.56)*(1-0.56)=0.8064