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#1 Help Me ! » statisitc probability » 2016-03-13 17:00:57

912324434
Replies: 2

Problem 4
In a university games tournament, 64 students are about to participate in a chess
knockout competition.
The first round consists of 32 games, with two students per game.
The 32 winners of the first round get to play in the second round, which consists of 16
games, and so on, until an overall winner is declared in the sixth round.
(In the case of a draw on any game, a coin is tossed to determine the winner.)
(a) In how many different ways can the 64 participating students be paired up
on the first round?
(Do not consider the order in which students can be paired up.)
(b) Suppose that the 64 participating players are of equal ability,
and pairing up is purely random on each round.
Find the probability that Eva and Brett (two of the 64 students)
will get to play each other at some stage during the knockout competition.

#2 Help Me ! » about statistics » 2016-03-13 16:59:53

912324434
Replies: 3

Problem 5
You are holding a party at home, and everyone is about to participate in the following
game.
Each person will write their name on a card. All the cards will then be collected and
randomly redistributed (one per person). If anyone gets back the card with their own
name, they will swap cards with the person closest to them in the room.
When everyone has a card with someone else’s name on it, you will call out the name
on your card. The called person will then call out the name on their card, and so on,
until finally your own name is called out.
If anyone’s name does not get called out at some stage during this game, they will
have to drink a whole 1 litre bottle of vodka by midnight.
(a) Suppose that there are five people at your party (including yourself).
Find the probability that no one will have to
drink 1 litre of vodka by midnight.
Then find the expected number of people
who will have to drink 1 litre of vodka by midnight.
(b) Derive general formulas for the probability and expectation in (a), ones which
are correct for any number of people attending your party (i.e. 2, 3, 4, etc).
Then apply these two formulas to the cases where there are 2, 3, 4, 5, 10
and 100 people at your party, respectively. Present your results in a table.

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