Five persons in a group of 20 are grauduate

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The discussion focuses on calculating probabilities related to selecting graduates from a group. For part i, the probability of selecting all graduates is calculated using the combination formula, specifically 5C3 divided by 20C3. In part ii, the probability of selecting at least one graduate is derived from multiple combinations of graduates and non-graduates, summing the probabilities of different scenarios. Participants are confirming the correctness of these calculations, referencing the Hypergeometric Distribution for guidance. The accuracy of the proposed solutions is the main concern of the discussion.
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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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