Question

Please help me check another answer ...

Walden has 4 children. What is the probability that 2 children are boys and 2 children are girls?

Answer 1

1/2 * 1/2 * 1/2 * 1/2

Answer 2

1/16 chance

Answer 3

Hmmm. that's not what I got or what's in the answer key.

Answer 4

The order isn't important, so it could be bbgg, bgbg, etc.

Answer 5

there are 2^4 total combinations.
then there are 4!/(2!2!) ways to have 2 boys and 2 girls. thats 6.
so 6/16 gives 3/8 ( i think)

Answer 6

I got what joemath got, but I used an unsophisticated tree diagram. Thanks for the confirmation though.

Answer 7

yep - i did same as mathdrills - 3/8 is correct

Answer 8

I agree with joe. There are 2^4 different permutations (with repetition) of b/g amongst 4 children.

Then of those we need to know how many different ways we can have 2 boys. So we can pick from the 4 different positions of order, 2 of them to be boys (or girls. Choosing one locks in the choice for the other).

The number of different ways we can pick these two spots for the boys (or girls) is \(4 \choose 2\) = 4!/(2!2!) = 6.

So yeah the probability is:

6/16 = 3/8