probability how many students are male and used marijuana in the past 6 months?

Question

I have been looking at these questions for a few hours now and I am very confused. any help would be very much appreciated :)  Even if you only help with one question that would be great too! thanks :) 

 

14. The following contingency resulted from data collected from class of 120 first-year University of Calgary students. Each student was asked their (i) gender and (ii) have they used marijuana in the past six months.
Male Female
Used marijuana 24 16
Not Used marijuana 35 45

Defining the events as:
M: a first-year student is a male
F: a first-year student is a female
Used: a first-year student has used marijuana in the past six months
NotUsed: a first-year student has not used marijuana in the past six months

From this data, re-express this contingency table converting the counts to probabilities. Use this `new' table to answers the questions below.

A)  Report the probability that a randomly chosen first-year student from this class is male and has used marijuana in the past six months.
B) Find the probability that a randomly chosen first-year student from this class is male or has used marijuana in the past six months.
C) Find the probability that a randomly chosen first-year student from this class is female and has not used marijuana in the past six months.

Answer 1

                   Male            Female            Totals

Used             24                  16                40

Not used        35                 45                 80

Totals             59                 61              120 <--- grand total


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Divides each stat by 120 to get the probabilities

                        Male                      Female                 Totals

Not Used             20%                      13.3%                   1/3=0.3 = 33.3%

Used                   29.16                     37.5%                   2/3= 0.6 = 66.6%                 

 

Totals                 49.16%                  50.83%                        100%

 

 

 

part A :   29.16%

 

part B: 49.16% + 37.5% = 86.6%

 

part C: 13.3%

Answer 2

A) Report the probability that a randomly chosen first-year student from this class is male and has used marijuana in the past six months.

 

That is 24 out of 120 students for a probability of 24/120 = 20%

 

B) Find the probability that a randomly chosen first-year student from this class is male or has used marijuana in the past six months.

 

That is Probability of being Male M plus Probability of using marijuana minus Probability of Male and using marijuana

 

(24+35)/120 + (24+16)/120 - 24/120 = 75/120=.625 = 62.5%

 

C) Find the probability that a randomly chosen first-year student from this class is female and has not used marijuana in the past six months

 

That is 24 out of 120 students for a probability of 45/120 = 37.5%

 

Note that this is 1-Probability that first-year student from this class is male or has used marijuana in the past six months.