there are 14 girls and 10 boys in an algebra 2 class. what is the probability of a group of 4 having 3 girls and 1 boy
We calculate the numerator of the probability, which is the number of
successful possibilities, of 3 girls and 1 boy.
The number of choices of 3 girls out of 14 girls, (14 choose 3), is C(14,3)
For every choice of 3 girls,
The number of choices of 1 boy out of 10 boys is (10 choose 1) or C(10,1)
So there are c(14,3)·C(10,1) choices of 3 girls and 1 boy.
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We calculate the denominator of the probability, which is the number of
all possibilites, successful or not, of any 4 people from the 14+10 or 24
people.
That's the number of choices of 4 people out of 24 people, (24 choose 4),
or C(14,3)
The desired probability is therefore
C(14,3)C(10,1) 364·10 3640 260
—————————————— = ———————— = ——————— = ————— ≈ 0.3425559947
C(24,4) 10626 10626 759
Edwin
