umaa wrote:What is the probability for a family with three children to have a boy and two girls, assuming the probability of having a boy or a girl is equal?

a)1/8
b)1/4
c) 1/2
d)3/8
e)5/8

IMO Answer is 3/8

There are 2^3 possibilities.

because each children can be of two options boy/girl.

3 ways has 1 boy and 2 girls - 3!/2!

so answer is 3/8

The person below me has give an even better method.I was making it complex

P(Boy) = P(Girl) = 1/2

There are 3 cases...

1. B,G,G = 1/2*1/2*1/2 = 1/8
2. G,B,G = 1/8
3. G,G,B = 1/8

P(1 Boy and 2 Girls) = 1/8 + 1/8 + 1/8 = 3/8


Am i right???

you are right bsandhyav

Isn't this 1/4?

The family has 3 children. The probability of having either a Boy or a Girl is equal. So, they could be having,

BBB
GGG
BGG
GBB

with no particular order. So it's 1/4. When we say the answer to be 3/8 we are necessarily saying that there are a total of 8 possibilities out of which 3 is suitable for this requirement. What are those 8?

BBB, GGG, BGG, GBG, GGB, BBG, BGB, GBB out of which bold ones are the required case, but this is not true as the order does not matter.

enniguy wrote:Isn't this 1/4?

The family has 3 children. The probability of having either a Boy or a Girl is equal. So, they could be having,

BBB
GGG
BGG
GBB

with no particular order. So it's 1/4. When we say the answer to be 3/8 we are necessarily saying that there are a total of 8 possibilities out of which 3 is suitable for this requirement. What are those 8?

BBB, GGG, BGG, GBG, GGB, BBG, BGB, GBB out of which bold ones are the required case, but this is not true as the order does not matter.

This is what I got. You can't use 1/2 for the last selection. Because there is only one option that we should choose one girl. So, it should be 1 instead of 1/2

The answer I got is, 1/2*1/2*1 = 1/4

enniguy wrote:Isn't this 1/4?

The family has 3 children. The probability of having either a Boy or a Girl is equal. So, they could be having,

BBB
GGG
BGG
GBB

with no particular order. So it's 1/4. When we say the answer to be 3/8 we are necessarily saying that there are a total of 8 possibilities out of which 3 is suitable for this requirement. What are those 8?

BBB, GGG, BGG, GBG, GGB, BBG, BGB, GBB out of which bold ones are the required case, but this is not true as the order does not matter.

Received a PM.

The issue here is that you are mistaking probabilities. In the series:

BBB
GGG
BGG
GGB

you made the mistake of giving every case a probability of 1/4. I'm guessing you were thinking: we have four cases and the total probability is always 1, so the probability of each case should be 1/4. The problem is that that's not correct. You yourself presented all the cases above and noted that there are 8 possible combinations:

BBB, GGG, BGG, GBG, GGB, BBG, BGB, GBB

As you can probably tell from the colors, there are "sets" of different possibilities:

BBB counts only once, since there's only one possible combination with three B's
GGG counts only once as above
BGG counts three times since there are three "combinations" that add up to this case (noted in black)
GBB similarly counts three times (color red).

Hope this helps.

@umaa: you are NOT allowed to choose from any options. Every childbirth is its own probability, like a coin toss. My second coin toss will be independent from my first coin toss and same goes for children, i.e. it doesn't matter if I get heads or tails the first time, since it doesn't affect my second toss.
So for each of the three events you have 50% chance of boy and 50% chance of girl. These are absolutely unrelated events! Any combination of three genders will result in a probability of 1/2*1/2*1/2 = 1/8, since the probability of a complex event happening is the product of all the probabilities of the events that make it up. As you guys have noticed, there are three favorable "gender combinations", so 3*1/8.

The first question you should ask yourself is whether order is important. In this case, it is not so you can have either:
GGB
GBG
BGG

with each a probability of 1/8 so 1/8*3 = 3/8

if order had been important - ie must get B between the 2 girls then 1/8 would have been correct...

(note however) if they would have said B is last, then you could have G1G2B or G2G1B so 2/8

Hope this helps