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) About Me  (Show Source):
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highlight%28In%29 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) = %2810%2F20%29%2A%289%2F19%29%2A%288%2F18%29%2A%287%2F17%29%2A%286%2F16%29 = 30240%2F1860480 = 21%2F1292.


P(all 5 are girls) = %2810%2F20%29%2A%289%2F19%29%2A%288%2F18%29%2A%287%2F17%29%2A%286%2F16%29 = 30240%2F1860480 = 21%2F1292  (the same value).


P(all are of the same sex) = the sum = 21%2F1292 + 21%2F1292 = 21%2F646 = 0.03251  (rounded).

Solved.




Answer by greenestamps(13200) About Me  (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.

P=%28C%2810%2C5%29%2BC%2810%2C5%29%29%2FC%2820%2C5%29

P=%28252%2B252%29%2F%2815504%29=21%2F646

(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.

P=%2820%2F20%29%289%2F19%29%288%2F18%29%287%2F17%29%286%2F16%29=3024%2F93024=21%2F646

ANSWER: 21/646