# Family Gathering

• Aug 26th 2008, 12:59 PM
Obsidantion
Family Gathering
If your parents, your parents' parents and your parents' parents' parents all shook hands with each other, how many handshakes would occur, provided that everyone in your family has 2 parents?
• Aug 27th 2008, 05:24 AM
Soroban
Hello, Obsidantion!

Quote:

If your parents, your parents' parents and your parents' parents' parents
all shook hands with each other, how many handshakes would occur,
provided that everyone in your family has 2 parents?

You have 2 parents, 4 grandparents, and 8 great-grandparents.

With 14 people, there are: .\$\displaystyle {14\choose2} \:=\:91\$ handshakes.

• Aug 27th 2008, 07:50 AM
Obsidantion
Quote:

Originally Posted by Soroban
Hello, Obsidantion!

You have 2 parents, 4 grandparents, and 8 great-grandparents.

With 14 people, there are: .\$\displaystyle {14\choose2} \:=\:91\$ handshakes.

Yes, good one.

Q1. If a couple in your family has 2 babies and at least 1 of the babies is a boy, what is the chance that both of the babies are boys?

Q2. If a couple in your family has 2 babies and the older of the 2 babies is a boy, what is the chance that the other baby is a boy as well?
• Sep 2nd 2008, 11:23 AM
Sun
Q1. If a couple in your family has 2 babies and at least 1 of the babies is a boy, what is the chance that both of the babies are boys?

Q2. If a couple in your family has 2 babies and the older of the 2 babies is a boy, what is the chance that the other baby is a boy as well?[/quote]

A1 : 75% chance. out of the 4 probabilities (girl followed by boy, girl followed by girl, boy followed by girl , boy followed by girl) , we know that girl can't be the first one. so two probabilities eliminated giving us a guarantee that the chance is at least 50%. At this point both Boy followed by girl or Boy followed by Boy has a 75% chance, as getting either a second boy or girl has 25% chance? (I think i'm confusing myself)

A2 : 50%. The second probability does not effect the first probability, unlike question 1...
• Sep 2nd 2008, 01:51 PM
Obsidantion
Quote:

Originally Posted by Sun
A1 : 75% chance. out of the 4 probabilities (girl followed by boy, girl followed by girl, boy followed by girl , boy followed by girl) , we know that girl can't be the first one. so two probabilities eliminated giving us a guarantee that the chance is at least 50%. At this point both Boy followed by girl or Boy followed by Boy has a 75% chance, as getting either a second boy or girl has 25% chance? (I think i'm confusing myself)

A2 : 50%. The second probability does not effect the first probability, unlike question 1...

Your second answer is right and for the right reason too.
The first question is hard, I was really confused when I first heard it. There are four possibilities (with equal chance) for the two babies' genders, like you said; girl then boy, girl then girl, boy then girl, boy then boy. Of these combinations, three have at least one boy, the other has two girls. Of the three combinations with at least one boy, only one of those has both babies as boys, which leaves a probability of one third as to how many of the combinations with at least one boy has two.