Original Problem:
Season tickets for men's basketball games cost graduate students $150 plus camping for a weekend. At this price, quantity demanded is 3 times quantity supplied, so a lottery is held at the end of the camp-out weekend. Lottery winners receive an entire season of tickets while losers receive nothing. Prior to learning who will win tickets, some students create groups in which they agree to divide the tickets evenly among the group. For simplicity, assume that there are 12 game tickets per season.
Does pooling change the mean number of game tickets that a student receives?
If two students agree to pool tickets, what are the odds that they will get some tickets (at least 1 set)?
This from Brian:
your odds of getting tickets for any PARTICULAR game (i.e., cal v ucla) should not change regardless of pooling or not, or the number of people in your pool.
Your odds of going to ANY game increases w/ pooling and the number of people your pool, up to 12 people. At more than 12 people the odds start to degrade according to some formula I have no desire to work out by some fraction, perhaps -1/12 per additional person?
My guess:
If you pool your resources then you increase your chance of winning but reduce the number of tickets you will win (if you do win). I guessed this because Supply = 3xDemand, so Demand = Supply/3. I figured for every 1 ticket package available (with 12 tickets), there are 3 students that want it. So your odds of winning are 1 in 3 (1/3).
Not sure what 'mean number of game tickets' is, so I can't answer that. If it is the chance of winning * the number of tickets you win, then for one person it is 1/3 x 12 = 4,
and it's the same whether you have 1, 2, 3 or however many people in your group.
for two people:
1/3 + 1/3 = 2/3 chance
2/3 chance * # tickets = 8 tickets
8 tickets / # people in group = 4
You have a 1/3 chance of winning, and your chance adds to their chance, so
1/3 + 1/3 + 1/3 = 1
1 * # of tickets = 12
12 / number of people in your group (3) = 4
If two students pool their resources there is a 2/3 chance they will get some tickets.
1/3 chance + 1/3 chance = 2/3
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No idea if any of this is right. I'll post the answer when I hear back from my friend about her homework.
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