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OpenStudy (anonymous):
@Mathematics 3 students are selected at random from a class consisting of 5 freshman, 3 sophomores, and 2 juniors. Find the probability that 2 freshman and 1 junior are selected given that at least 1 freshman is selected.
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OpenStudy (anonymous):
good problem, reminds me of my school days
OpenStudy (anonymous):
axiomatic way is better, what it asks is \[P(F= 2 , J = 1 | F \geq 1)\] which is same as \[P(F = 2, J =1 , F \geq 1)/P(F \geq 1)\] \[= \frac{P(F = 2, J =1)}{P(F = 1 ) + P(F =2) + P(F=3)}\] Now find the probabilities in the following way: \[P(F = 2, J = 1) = P(J =1)P(F = 2 |J = 1) = \frac{2}{10} \cdot \frac{5}{9} \cdot \frac{4}{8}\] and so on. Hope this helps
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