Dream Weaver wrote:. The probability of having a girl is identical to the probability of having a boy. In a family with three children, what is the probability that all the children are of the same gender?
a) 1/8.
b) 1/6.
c) 1/3.
d) 1/5.
e) 1/4.
Both approaches noted are great and, in a simple question like this, effective ways to solve the problem.
We could also recognize that this is a pseudo coin-flip question. Any time you see 50/50 binary situations, think coin flips!
The question could have been:
if a fair coin is flipped 3 times, what's the probability of getting either exactly 3 heads or exactly 3 tails?
So, we could have applied the coin flip formula, which is:
Probability(k results out of n flips) = nCk/2^n
Since we want 3 heads OR 3 tails, we calculate the probability of each and ADD them together:
3C3/2^3 + 3C3/2^3 = 1/8 + 1/8 = 1/4
You also could have brute forced the question, much like you can with 3 coin flip questions. The possibilities are:
BBB
BBG
BGB
BGG
GBB
GBG
GGB
GGG
and 2 out of the 8 match what we desire, so 2/8 or 1/4 is the right answer.
