Interesting question

Hello,

Not sure if this is the right board to put this in. An interesting question came up on which outcome would be more or less probable

Situation A - winning the powerball 1 in 195,249,054
Situation B - Three women from the same family having a boy that is exactly 4 days away from their birthday. (so far we have two out of three with this and the third one has a due date that matches which is where the conversation came from)

So far here's where I'm at. Thanks for any help in pointing me in the right direction.

There's two shots to hit the target date multiplied by three people to hit it

2/365 x 2/365 x 2/365 = 8/48,627,125 or 1/6,078,390.625

Now here's where I get lost. for the purposes of this math we assume 1/2 the time it will be a boy and 1/2 the time a girl so

1/6,078,390.625 x 1/2 = 1/12,156,781.25 but we need it to be a boy three seperate times so would the proper equation be??

1/6,078,390.625 X 1/2 x 1/2 x 1/2 = 1/48,627,125???

Now I need to find a way to take into account that it needs to be three women from the same family so I was thinking that we could work from a base assumption that we would only include families with three women (unless you know how to account for this). I'm not really sure how to do this and was wondering if anyone could help?

Maybe I'm totally off and someone won't mind setting me straight.

Thanks for any that take a stab at it.

well, my thoughts are that if the birth date has to be exactly 4 days of the mothers', then the ratio would be 2/365. As you've said. Then assuming 1/2 for the boy, it's probably more like 0.45, better odds of getting a girl. So you would get..

\(\displaystyle \left(\frac{2}{365}*\frac{1}{2}\right)^3\)

Then multiply that number by the probability that a family has 3 daughters (you'd have to look that up.) How to phrase the question would be, "If the probability of a family bearing 3 daughters is x. What is the probability that a family with 3 women, who have 1 boy each, exactly 4 days from their respective mother's birthdays." or something like that. I don't think that factoring in the 3 daughters in a family probability is valid for this problem. It would be more appropriate from a statistical standpoint to say "any three women"