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 June 1st, 2017, 04:44 PM #1 Senior Member   Joined: Nov 2015 From: hyderabad Posts: 206 Thanks: 2 Probability2 Three students are selected at random from a class of $10$ students among which $4$ students know $C$ programming of whom $2$ students are experts. If every such selection is equally likely, then the probability of selecting three students such that at least $2$ of them know $C$ programming with at least one out of the two selected being an expert in $C$ programming is A)less than $1/4$ B)Greater than $1/4$ but less than $1/2$ C)Greater than $1/2$ but less than $3/4$ D)Greater than $3/4$ I got the answer $1/2$ after calculation, but there seems to be no exact option for it. Please check. Thank you
June 1st, 2017, 05:05 PM   #2
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Quote:
 Originally Posted by Lalitha183 Three students are selected at random from a class of $10$ students among which $4$ students know $C$ programming of whom $2$ students are experts. If every such selection is equally likely, then the probability of selecting three students such that at least $2$ of them know $C$ programming with at least one out of the two selected being an expert in $C$ programming is A)less than $1/4$ B)Greater than $1/4$ but less than $1/2$ C)Greater than $1/2$ but less than $3/4$ D)Greater than $3/4$ I got the answer $1/2$ after calculation, but there seems to be no exact option for it. Please check. Thank you
Let non-programmers be denoted by N, programmers by P, experts by E.

Valid combinations are

NPE, NEE, PEE, PPE

so the probability of any of these combos is

$\dfrac{ \binom{6}{1}\binom{2}{1}\binom{2}{1}+ \binom{6}{1}\binom{2}{0}\binom{2}{2}+ \binom{6}{0}\binom{2}{1}\binom{2}{2}+ \binom{6}{0}\binom{2}{2}\binom{2}{1}}{\binom{10}{3 }} = \dfrac{17}{60}$

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