A mom has 8 children. 7 boys and the youngest (8th) is a girl. “The chances of the 8th as a girl are 50/50,” (right?) what about overall–still 50%?
I get 3/time Netflix. I order a 6 disc series. I open the first 3, in order, 1-2-3. Then I open the next 3 in order, 4-5-6. What are the chances of that?
I hope I don’t seem dumb here–I’m just trying to show off my math skills (via exploiting the math people here).
I don’t know what you mean by “overall.”
There’s a 1/3 chance you’ll open #1 first, then a 1/2 chance you’ll open #2 second, so 1/6 of opening 1-2-3. Same logic for 4-5-6. overall it’s 1/6*1/6, so 1/36.
What do you mean “What about overall”? You mean what are the odds that it comes out b-b-b-b-b-b-b-g? It’s .5*.5*.5*.5*.5*.5*.5*.5=.5[sup]8[/sup]=1/256.
There are 3 ways to choose the first disc, 2 ways for the second, one way for the third, three ways for the fourth, two ways for the fifth, and one for the sixth. So 32132*1 = 36. So 1 out of 36 chance of that pattern.
ETA: Scooped by PP. OP, please familiarize yourself with the multiplication counting principle.
The first question is 50%, if you assume that gender of children is uniformly random. It might not be. The overall distribution is (approximately) equal numbers of each, but it might be the case that some parents are more likely to have boys, and some parents are more likely to have girls. If we knew how common such biased parents were, and how large the bias could be, then we could determine the probability that the parents in question are biased parents, and from there determine the probability for their next child.
For the second question, likewise, we have to assume that you’re opening the discs in random order, but that might not be a good assumption. They’re probably in numerical order in your queue, and it’s quite reasonable that Netflix might put them in the mail in the same order as they were in your queue, and that you might order them in the order they were mailed in.
The chance that a woman’s youngest child is a girl is 50-50.
The chance that she is starting a family and would have 7 boys and then a girl is as pointed out above, 1/256. Or the odds that some randomly chosen mother-of-8 has that configuration of family…
The chance that a woman who ALREADY HAS 7 boys will have a girl is 50-50.
The question is - what are you asking for odds on, and what’s fixed and certain already?
I assume Netflix is smart enough to not reship what you’ve already seen; and that you are talking about a single envelope with 3 discs in it, and you don’t care if it’s 123, 132, 312, etc.?
So what are the odds that netflix will pick a specific 3 out of 6, order not important? (sort of like picking the balls in a lottery, pick 3 of 6).
There are 6! (6 factorial =720) possible combinations of 6 items. There are 3! (= 6) possible ways to arrange the first 3 to be what you want. So 3!/6! = 6/720=1/120 ways to arrange this pick of 1,2,3. However, the order of 1,2,3 does not matter, so that’s 3!/120 or 1/20 odds.
then the next envelope, you get the rest of the discs, 4,5,6.
nm
If you know that the eighth child is a girl, then the chances that the eighth child is a girl are 100%. If you only know that the woman has seven boys, the chance that the eighth is a girl is probably less than 50%, as children are not coin flips.