Question

A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, job, recreation, or other.

	Homework	Job	Recreation	Other
Male	29	35	23	9
Female	18	43	39	4

a. If one student is randomly chosen from the group, what is the probability that the student is male?
b. If one student is randomly chosen from the group, what is the probability that the student chose "recreation" as their most likely activity on a Saturday morning?
c. If one student is randomly chosen from the group, what is the probability that the student is male and chose "job" as their most likely activity on a Saturday morning?
d. If one student is randomly chosen from the group, what is the probability that the student chose "recreation" or "other" as their most likely activity on a Saturday morning?
e. If one student is randomly chosen from the group, what is the probability that the student is female or chose "homework" as their most likely activity on a Saturday morning?
f. Find the probability that a college student from the group chose "homework" as their most likely activity on Saturday mornings given that they are male.

Answer 1

Total = 29 + 35 + 23 + 9 + 18 + 43 + 39 + 4 = 200

a) P(male) = (29 + 35 + 23 + 9)/200 = 96/200 = 0.48

b) P(recreation) = (23 + 39)/200 = 62/200 = 0.31

c) P(male and job) = 35/200 = 0.175

d) P(recreation or other) = P(recreation) + P(other) - P(recreation and other)

                                   = (62 + 13 - 0)/200 = 75/200 = 0.375

e) P(female or home work) = P(female) + P(home work) - P(female and home work)

                                       = (104 + 47 - 18)/200 = 133/200 = 0.665

f) P(homework) = (29 + 18)/200 = 47/200 = 0.235