prachich1987 wrote:What is the probability for a family with three children to have a boy and two girls (assuming the probability of having a boy or a girl is equal)?
a) 1/8
b) ¼
c) ½
d) 3/8
e) 5/8
Source : some online material
The explanations provided are great, I just wanted to add that this is an example of what we sometimes call a "pseudo-coin flip question".
In other words, the question is identical to:
If a fair coin is flipped 3 times, what's the probability of getting exactly two heads?
Once you recognize it as a coin flip problem, you can apply the coin flip formula to solve:
The probability of getting k results on n flips is:
nCk/2^n
(nCk = n!/k!(n-k)!, the combinations formula).
For this particular question, the other solutions may very well be quicker (remember, just because there is a fancy formula doesn't mean that algebra is the best approach to a problem), but the formula is useful on more advanced coin flip/pseudo-coin flip questions.
