SOLUTION: A class of 10 boys and 10 girls a committee of 5 are choosen. What is the probability that all are of the same sex?

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Question 1202550: A class of 10 boys and 10 girls a committee of 5 are choosen. What is the probability that all are of the same sex?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
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a class of 10 boys and 10 girls a committee of 5 are chosen. What is the probability that all are of the same sex?
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P(all 5 are boys) =  =  = .


P(all 5 are girls) =  =  =   (the same value).


P(all are of the same sex) = the sum =  +  =  = 0.03251  (rounded).

Solved.




Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Here are two basic ways of solving this problem.

(1) Using the basic definition of probability

The good outcomes are either selecting 5 of the 10 boys or 5 of the 10 girls; the possible outcomes are selecting 5 of the 20 students.





(2) Choosing one student at a time and multiplying the probabilities that the desired outcome is obtained. The first student chosen can be any of the 20 students; after that, the next four students chosen must be the same sex as the first.



ANSWER: 21/646
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