MATHS CLASSES: WEDNESDAY 26.10

[charlieeppes.livejournal.com]

Charlie is surrounded by a stack of old books, crumpled pieces of paper, and pencils. He's writing eagerly on one of the blackboards. The heading he's written is: Probability Calculation: Migrasjon.

He waits until everybody in a group has arrived. "Joan Girardi and Kimberly Shaw are no longer enrolled in this class and have possibly been eaten. This means that there's an open place in Intermediate, if you know of anyone who might wish to join us.

This is the attendance I have counted thus far, please let me know if I have made any mistakes." He gives them all a copy of their attendance record, as well as todays problems.

Comments

Re: Intermediate

[http://users.livejournal.com/___lily_evans_/]

"You've lost me," Lily said.

Re: Intermediate

[notstakedyet.livejournal.com]

"We're focusing just on the general odds of them ever getting the numbers," Angelus said, becoming more animated as he figured it out. "What we're forgetting is that the bet is that they get the numbers first."

He started to write out the possibilities on a fresh piece of paper. "See, A says he can roll 12 first. B says he can roll 7 first and second. More important, they're betting against each other. In games like that you don't just win if you win, you win if the other guy loses. And our boy B has more chances to lose because he stupidly bet on two 7s in a row. There's more odds of him not getting those double 7s than there are for A to get the 12 once."

Re: Intermediate

[http://users.livejournal.com/___lily_evans_/]

"Wait, but isn't that still the same thing? - I mean, we did the math," Lily says getting frustrated. "The odds of winning for both are one in thirty-six. The odds of losing for both are thirty-five in thirty-six. I feel like I see what you're saying, but I don't."

Re: Intermediate

[notstakedyet.livejournal.com]

"The odds of losing look like they're the same but they're not," Angelus said. He wrote more numbers down. "Look, if the first roll is 12 our boy A takes the pot, right? 1/36 odds of happening. But here's the thing, if neither 7 nor 12 comes up, A still has a nice pile of cash to take home to his lady. A wins because B loses and that has - " Angelus frowned as he tried to do the math in his head. "29/36 odds of happening. I think.

"And that's just that one roll. Let's say our boy B has good luck and rolls 7 first time around. If the second roll isn't a 7 and is maybe even a 12 then A's eating steak for dinner again. A's chances of winning stack up higher when you take into account not just the 12, but all the time it's not 7."

Re: Intermediate

[http://users.livejournal.com/___lily_evans_/]

Lily almost got what he was saying, but it just wasn't completely clicking yet. "Right... and at least the 12 has some chance of winning on every next roll, where the 7 only has a chance of winning after a 7 has just been rolled..."

Re: Intermediate

[notstakedyet.livejournal.com]

"Exactly," Angelus said. "Though it's not as obvious as flipping the odds of B winning. It's figuring out the odds of A winning on 12 combined with the odds of B losing those 7s. Get those and we'll have our answer."