Expert: Paul Klarreich - 10/20/2010

Question
5 families have 3 children.
find the probability that
(i) atleast 1 of these families has 3 boys.
(ii) each family has more boys than girls.

Answer
Questioner:   athena
Country:  Australia
Category:  Advanced Math
Private:  No
 
Subject:  probability
Question:  5 families have 3 children.
find the probability that
(i) atleast 1 of these families has 3 boys.
(ii) each family has more boys than girls.
................................
(1) Any time you have an "at least one of" situation, make it
the complement of "none of these".

So figure the p(a family does not have three boys) = 7/8.
Then p(all five families do not have three boys) = (7/8)^5
and p(at least one has 3 boys) = 1 - p(all five families do not
have three boys)

(2) What do you think is p(a given family has more boys)?  

Before you answer, what do you think is p(a given family has
more girls)?

Before you answer that, what do you think is p(a given family
has equal numbers), given that each family has 3 children?

Now that you know that for a single family, what is p(all five
have more boys)?