posted by Angela
Assume a family is planning to have three children.
1. Why do probabilities centered around this scenario represent the same probabilities as those for flipping three coins
in flipping one coin, and having one child:
prob(heads) = 1/2, prob(tails) = 1/2
prob(boy) = 1/2 , prob (girl) = 1/2
for flipping 3 coins, or considering 3 kids:
prob(1 head, 2 tails) = 3(1/2)^3 = 3/8
prob(1 boy, 2 girls) = 3(1/2)^3 = 3/8
This is because each pregnancy is independent of the others so the chances of receiving either a boy or girl is 50% for each separate pregnancy. the same as flipping three coins, the chances of having either heads or tails is 50% and each flip is independent of the others.