SOLUTION: Task 21. From the group of students, in which 18 boys and 12 girls, two people are elected to the faculty council. What is the likelihood that there will be at least one young man

Question 1160047: Task 21. From the group of students, in which 18 boys and 12 girls, two people are elected to the faculty council. What is the likelihood that there will be at least one young man among the elect?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
What is the probability that there will be NO man.
This means that both are women
The denominator is choosing 2 from 30 or 30C2=435
the numerator is 18C0, which =1, times 12C2=66
the answer 1-(66/435) or 369/435=0.8483
Do this more simply by recognizing the probability of the first being a woman is 12/30 and the second is 11/29
for a product of 132/870 or 0.1517. Everything else is at least one man or 1-0.1517 or 0.8483
Can check this crudely.
40% are women or 2/5. The likelihood of both women is approximately (2/5)^2=4/25=0.16
Otherwise, they are men, and 1-0.16=0.84, close to what was obtained.
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