This thread is just what the title says it is. It is all about Math. You can post math jokes(the jokes don't have to be good), math questions, what you like about Math, or even why you hate Math.
My math joke: Resistance is not futile. It is voltage divided by amps.
Ummm well I already read this whole math thread so I know that the answer is 0. And, I know 103 digits of Pi. 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798 I used to know more but I forgot about a dozen.
Interesting math thing of the day: Ulam's spiral. Look it up, it's pretty cool.
It is black side up. What is the probability that the other side is red? Why?
I have 2 quick guesses.
There are 3 red sides, and 3 black. So once we pick a black side, there are 2 black and 3 red. So there's a 60% chance of red, and 40% chance of black.
Other guess
There's a 1/3 chance you chose the red and black card, so there's a 33.3% chance.
Another question: Given that one side is black, what is the probability that you picked the red-black card? Why?
Is it? If one of the sides is black, then you clearly did not pick the red-red card. Which leaves two choices, red-black or black-black. Meaning there is a 1/2 chance you got the red-black.
It turns out the two questions don't have the same answer. Why?
Oh, i get it. The first one is asking what the chances the other side is red, not the chances it is the red and black card. It makes the rules that there is an R&R, an B&B, and a R&B card partly pointless, all you need to know is that there are 3 of each colors. Doesn't this mean my previous answer is right?
Well, 1/3 is the correct answer for this first question. But I'm not too sure on your reasoning. I mean, asking what the chances the other side is red is the same thing as asking what the chances the card is the black red card.
The questions differ because the first one specifies that that the card is drawn black side up. And the second only specifies that there is a black side.
Well, 1/3 is the correct answer for this first question. But I'm not too sure on your reasoning. I mean, asking what the chances the other side is red is the same thing as asking what the chances the card is the black red card.
My reasoning was probably wrong and didn't make any sense, I'm just throwing guesses.
If the card is black side up, then you know it can only be one of two cardsâ"either the black-black card, or the black red card. However, it is less likely for the red-black card to be drawn black side up than for the black-black card. So this is how the probability goes:
For each card there's a 50/50 chance it was picked. For each card there's a 50/50 chance that the up-side (for explanation's sake let's say the up-side is black on the black-red card) will be drawn. So with the black-red card, of the 50% chance that it was picked, 100% of those outcomes result in the black side being up. With the red card that only happens 50% of the time it is picked. Therefore yes, it is 1/3. I'm kind of confusing myself as I say this but I believe the answer is 1/3. And I do sort of understand how to two questions are different. I'll think about this more and hopefully someone will come up with a good answer/explanation.
If the card is black side up, then you know it can only be one of two cardsâ�"either the black-black card, or the black red card. However, it is less likely for the red-black card to be drawn black side up than for the black-black card
That's exactly it! Here's a more concise way of explaining it, though:
If you pick a card black side up, one of three things happened: 1) You picked the black-red card black side up 2) You picked the black-black card black side up 3) You picked the black-black card with the other black side up.
The only event that matches our desired outcome is the first one. And all events are equally likely (specifically, all events have a 1/6 probability).
Therefore, since there are three possible events, and one desired event, the probability is 1/3.
These two questions come from a quiz in my probability class. The question was written like my first question, but most of the class answered it like it was the second question. In fact, even my teacher regarded it as the second question.
Since it was a probability class, most of the students were econ majors, and a few were math majors (including myself). Every single math major got the question correct, and we all argued with the professor about it for about 15 mins. They next day, the professor admitted that we were, in fact, correct.
Anyway, I just this was an interesting problem, with the two questions highlighting the importance of paying attention to detail. In math, every word matters.
