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# Statistical Events

12) The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Major Male Female Totals
Physics 25 25 50
Chemistry 60 40 100
Geology 30 20 50
Totals 115 85 200

Suppose a person is selected at random from these graduates. Consider the following events:
M: The person is a male.
F: The person is a female.
P: The person graduated in physics.
C: The person graduated in chemistry.
G: The person graduated in geology.
Find:
a) P(M)
b) P(M|P)
c) P(C and F)
d) P(C|F)
e) P(C and G)
f) P(C or G)
g) Are events C & F independent? Give a reason for your answer.

#### Solution Preview

a) P(M)
<br>Solution. Since there are 50+100+50=200 graduates, of them there are 115 who are male. So, P(M)=115/200=0.575
<br>
<br>b) P(M|P)
<br>
<br>Solution. Since there are 50 graduates from major physics, among them there are 25 who are male. Thus,
<br>P(M|P)=25/50=0.5
<br>
<br>
<br>c) P(C and F)
<br>
<br>Solution. ...

#### Solution Summary

12) The physical science degrees conferred by a school between 1992 and 1995 were broken down as follows:
Major Male Female Totals
Physics 25 25 50
Chemistry 60 40 100
Geology 30 20 50
Totals 115 85 200

Suppose a person is selected at random from these graduates. Consider the following events:
M: The person is a male.
F: The person is a female.
P: The person graduated in physics.
C: The person graduated in chemistry.
G: The person graduated in geology.
Find:
a) P(M)
b) P(M|P)
c) P(C and F)
d) P(C|F)
e) P(C and G)
f) P(C or G)
g) Are events C & F independent? Give a reason for your answer.

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