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.
