# Probability question :)

• Jul 11th 2011, 02:24 PM
somster100
Probability question :)
Just a question which i would like someone to confirm for me
for #a. i got 1/8 and #b. is larger (but i have no explination)

hopefully someone can kindly help me out :) <3

4) Your new neighbour moved in recently. The family consisted of the mom, the dad, and 3 kids. You knew there were 3 kids because you could always hear 3 kids’ voices through the building’s thin wall, but you didn’t know their gender because all 3 kids were still very young, in elementary school. You’ve seen the mom and dad. They look very much alike! So you expect the kids to look relatively alike as well.

a) Out of curiosity one day you decided to see how many boys and girls (not counting the parents) were in the family, so you went to knock on their door. And 1 boy came out. What is the probability that all 3 kids are boys given that 1 came out?

b) Of course you still didn’t have enough information to decide on all the 3’s gender, so you found some other excuse to knock on their door. A boy came out, but you couldn’t be sure if it was the same as the previous one or a different boy. Is the “probability that all 3 kids are boys” larger or smaller than part a)’s answer? Please explain your reasoning in a few sentences.

• Jul 12th 2011, 03:03 PM
Nemesis
Re: Probability question :)
Quote:

Originally Posted by somster100
Just a question which i would like someone to confirm for me
for #a. i got 1/8 and #b. is larger (but i have no explination)

hopefully someone can kindly help me out :) <3

4) Your new neighbour moved in recently. The family consisted of the mom, the dad, and 3 kids. You knew there were 3 kids because you could always hear 3 kids’ voices through the building’s thin wall, but you didn’t know their gender because all 3 kids were still very young, in elementary school. You’ve seen the mom and dad. They look very much alike! So you expect the kids to look relatively alike as well.

a) Out of curiosity one day you decided to see how many boys and girls (not counting the parents) were in the family, so you went to knock on their door. And 1 boy came out. What is the probability that all 3 kids are boys given that 1 came out?

As you already know the first child's gender, the options left to you for the other two kids are B-B, B-G, G-B, G-G, with B = boy, G - girl, hen is 1 out of4 or probability = $0.25$
Nemesis

b) Of course you still didn’t have enough information to decide on all the 3’s gender, so you found some other excuse to knock on their door. A boy came out, but you couldn’t be sure if it was the same as the previous one or a different boy. Is the “probability that all 3 kids are boys” larger or smaller than part a)’s answer? Please explain your reasoning in a few sentences.

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• Jul 12th 2011, 03:55 PM
Re: Probability question :)
Quote:

Originally Posted by somster100
Just a question which i would like someone to confirm for me
for #a. i got 1/8 and #b. is larger (but i have no explination)

hopefully someone can kindly help me out :) <3

4) Your new neighbour moved in recently. The family consisted of the mom, the dad, and 3 kids. You knew there were 3 kids because you could always hear 3 kids’ voices through the building’s thin wall, but you didn’t know their gender because all 3 kids were still very young, in elementary school. You’ve seen the mom and dad. They look very much alike! So you expect the kids to look relatively alike as well.

a) Out of curiosity one day you decided to see how many boys and girls (not counting the parents) were in the family, so you went to knock on their door. And 1 boy came out. What is the probability that all 3 kids are boys given that 1 came out?

In birth order, the children may be born in the following arrangements

BBB
BBG
BGB
GBB
BGG
GBG
GGB
GGG

7 of these birth orders contain boys
and in only 1 of these do we have 3 boys

So the probability of the 3 children being boys if 1 is a boy is 1/7.