Someone check my work, please?

Question

If a couple has 8 children, what is the probability that 5 of them are female?

Okay, so I used Pascal's triangle for this one. I looked at the 8th row and took the first 5 numbers and added them.

1 + 7 + 21 + 35 + 35 = 99

Then I put that number on top of 2^8 to get: 99/256

Did I do that right, or did I go about it the wrong way?

Thanks.

Answer 1

Not quite. Don't forget that the first row and digit are counted as number zero.

The 8th row is:
1 8 28 56 70 56 28 8 1

As well, the answer depends on the question. Does it mean 'at least 5 are female' or 'exactly 5 are female?

Solution:

The probability of getting this one sequence is going to be 1/2^8.

This is the point where you can use pascal's triangle. Remembering that the first row and digit are counted as number zero, select the 8th row.

1 8 28 56 70 56 28 8 1

To determine the probability that there will be 'exactly' 5 girls choose the 5th number. (don't forget zero) "56" and divide by the probability of a sequence (2^8)

56/256

The probability of there being 'at least' 5 girls is the probability that there will be 5 girls, plus the probability that there will be 6 girls, plus the probability that there will be 7 girls, plus the probability that there will be 8 girls.

56/256 + 28/256 + 8/256 + 1/256 =
(56+28+8+1)/256 = 93/256

Good luck!!

Answer 2

You have to take the 6th number from the 9th row: row 8 belong to selecting from 7 items.

8!/(5! * 3!) = 56

The probability is 56/256 = 7/32

Answer 3

Amit is right....