Question 358426
If four faculty members are randomly chosen, what is the probability that you choose four men or four mathematics instructors?
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Let A=Event of selecting four men
Let B=Event of selecting four math instructors
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basics of probabilities
P(AUB)=P(A)+P(B)-P(AnB)
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selecting 4 men:  P(A)=12C4*6C0/18C4
explanation: There are 18C4 of selecting 4 individuals from the 18
             of these, there are 12C4 of selecting the 4 men and 6C0
             of selecting 0 women
P(A)=495*1/3060=0.162
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selecting 4 math instructors P(B)=10C4*8C0/18C4
explanation: There are 18C4 of selecting 4 individuals from the 18
             of these, there are 10C4 of selecting the 4 math instructors
             and 8C0 of selecting 0 non-math instructors
P(B)=210*1/3060=0.069
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selecting 4 who are both male and math instructors
P(AnB)=6C4*12C0/18C4
explanation:  There are 18C4 ways of selecting 4 individuals from the 18
              There are 6C4 of selecting 4 of the 6 who are both male/math
               and 12C0 of selecting 0 who are the others.
P(AnB)=15/3060=0.005
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answer P(AUB)=P(A)+P(B)-P(AnB)=0.162+0.069-0.005=0.226