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

Intermediate

[charlieeppes.livejournal.com]

Two players bet on the total roll of two standard dice.  Player A bets that a 12 will be rolled first.  Player B bets that two consecutive 7s will be rolled first.  The players keep rolling until one player wins.  What is the probability that A will win?

Re: Intermediate

[sogothcally.livejournal.com]

*scribbles down the long division, and the dice probabilities*

It's almost a 50-50 split for who wins, if I've got my figures right.

Re: Intermediate

[cantgetnorelief.livejournal.com]

*tosses a gumball into Cally's lap*

Re: Intermediate

[sogothcally.livejournal.com]

*looks over at Anders, smiling, and pops the gum in her mouth and starts chewing*

Re: Intermediate

[12parseckessel.livejournal.com]

It's even odds. There's a 1 in 36 chance A's will come up. And a 1 in 6 that the first seven will show. But after that, there's still only a 1 in six that a second seven will show.

It's equal.

Re: Intermediate

[notstakedyet.livejournal.com]

Angelus chewed the end of his pen thoughtfully. Years of gambling had given him a gut instinct that A would be more likely to win, but damned if he knew the whys of it.

He looked around to see if his study buddy was nearby.

Re: Intermediate

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

"Sorry I'm late," Lily says, taking the seat next to Angelus.

Re: Intermediate

[notstakedyet.livejournal.com]

"No problem," Angelus gave her a friendly smile, shifting over to make room for Lily. He showed her his notes so far. They mainly involved a lot of numbers crossed out. "I want to say it's the first player. I just don't know why."

Re: Intermediate

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

Lily looked over the notes and started talking it through. "You'll have to help me out with this one - a standard die has... six sides? And so..." she adds some scribbles to the page without making much progress.

Re: Intermediate

[notstakedyet.livejournal.com]

"Yeah," he said. "Object of the game is to try to get the dice to come up with the numbers you need." He grinned. "I'm assuming for the example that they're not weighted."

Re: Intermediate

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

Lily looks confused. "Right... because weighted dice would...?"

Re: Intermediate

[notstakedyet.livejournal.com]

"Oh," Angelus said, realizing the scope of the culture difference. He began to sketch a six-sided die on his notebook paper. "They'd be more inclined to come up with a specific number, which makes them useful for cheating. But with regular dice you've got one in six odds of any number coming up. See? Each side gets a dot to indicate what the number is."

Re: Intermediate

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

Lily smiled gratefully. "Thanks."

She took out a fresh sheet of paper and started writing:

Player A:
6/6 = [1 in 6] x [1 in 6] = [1 in 36]

"Does that look right?"

Re: Intermediate

[notstakedyet.livejournal.com]

"So far," Angelus said.

Re: Intermediate

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

"Okay, and then Player B wants to get sevens, so that could be 2 and 5, 3 and 4, 1 and 6... and the reverse of those, right? Six possible combinations?"

Re: Intermediate

[notstakedyet.livejournal.com]

"Right again," Angelus said, looking like he was starting to understand where she was going with this.

Re: Intermediate

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

Lily writes some more:

1/6, 6/1, 2/5, 5/2, 3/4, 4/3
Each= [1 in 6] x [1 in 6] = [1 in 36]

[1 in 36] x 6 = [1 in 6]

"So it's a one in six chance of rolling a seven on the first try."

Re: Intermediate

[notstakedyet.livejournal.com]

"Seems to be," Angelus said. "But what about the second?"

Re: Intermediate

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

"Would it be the exact same odds for the second roll? And then we'd have to add... no, multiply those together?"

Re: Intermediate

[notstakedyet.livejournal.com]

"Pretty sure it's multiply," Angelus said.

Re: Intermediate

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

"Okay, so..."

[1 in 6] x [1 in 6] = [1 in 36]

"The odds are the same? That just doesn't seem right. Did we miss something?"

Re: Intermediate

[notstakedyet.livejournal.com]

[ooc: BTW, you are an angel, no pun intended, for walking him through this. He'll have an opinion if she says it's an even chance or odds in favor of player B, but there's no way I could keep him IC and say he could figure that out based on knowing the formulas. Knowing gambling OTOH... ahh, that's a different story.

Just so you don't think he's not contributing anything to the study buddy party ;) ]

Re: Intermediate

[cantgetnorelief.livejournal.com]

Anders chews on his pen and takes a long gulp of coffee for help. He ends up deciding that player B's going to win, just because life is weird that way. Also, his brain's not all here.

Re: Intermediate

[threeweapons.livejournal.com]

"It's going to be equall chance. One in thirty-six that a certain number will get rolled. One in thirty-six that a certain number gets rolled twice."

Re: Intermediate

[2ls-in-oneill.livejournal.com]

I'd say he's got a fifty-fifty shot of winning. Anyone who's ever played dice knows that rolling the same number twice when you want it is harder than it looks.