Five persons in a group of 20 are grauduate

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SUMMARY

The discussion centers on calculating probabilities involving a group of 20 individuals, of which 5 are graduates. The first part of the solution correctly applies the hypergeometric distribution to find the probability that all selected individuals are graduates, using the formula P(all graduates) = 5C3 / 20C3. The second part also correctly calculates the probability of selecting at least one graduate, employing the hypergeometric distribution with the formula P(at least one graduate) = (5C1 * 15C2 / 20C3) + (5C2 * 15C1 / 20C3) + (5C3 * 15C0 / 20C3.

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Question:
Five persons in a group of 20 are grauduate. If 3 are picked out of 20 at random,
i) compute the probability that all are graduate
ii) find atleast one being graduate.

Solution:

i) P(all grauduate being selected) = 5C3 / 20C3 [Is this correct]

ii) P(atleast 1 being graduate) = (5C1 . 15C2 / 20C3) + (5C2 . 15C1 / 20C3) + (5C3 . 15C0 / 20C3) [Is this correct]
 
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Hint: Hypergeometric Distribution.
 
Dickfore said:
Hint: Hypergeometric Distribution.


Need to know if the answer are correct or no
 

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