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Probability

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Probability

by arorag » Sat Jul 19, 2008 5:03 pm
From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected?
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by egybs » Sat Jul 19, 2008 6:18 pm
First we need to find the total number of possible groups:

6C4 (6 total children, picking a group of 4) = 6!/(4!*2!) = 15

So there are 15 different groupings possible.

Now we need to find out how many different groups there are with 2 boys and 2 girls. To get these groups, we need to pick 2 out of the 3 boys and 2 out of the 3 girls. So we need to know how many different ways you can select the two boys and how many ways you can select the 2 girls and multiply those together to get total number of possible groups... So:

3C2 * 3C2 = 3!/(2!*1!) * 3!/(2!*1!) = 3*3 = 9

Therefore: 9/15 = 3/5 or 60%
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