As a fundraiser, a local GAA club runs a lotto-type draw in which 4 numbers are drawn from 20: Mathematic Course Work, TCD, Ireland
| University | Trinity College Dublin (TCD) |
| Subject | Mathematics |
- a) As a fundraiser, a local GAA club runs a lotto-type draw in which 4 numbers are drawn from 20. As well as paying out a prize for a ticket with all four winning numbers, the club also refunds the price of any ticket which has none of the winning numbers. How many different tickets are there, and how many of them will have none of the four winning numbers?
b) At the end of each season, two soccer leagues have an inter-league knock-out tournament between the top 4 teams in each league – in which the winners of each league play the 4th team in the other and the runners-up play the 3rd team from the other league. If one league has 10 teams and the other league has 12 teams, how many different possible quarter-final line-ups are there? - An Average die has six faces; one of each showing 2 & 5, and two of each showing 3 & 4.
a) Two average dice are rolled together, one of them is red and the other is blue. Tabulate the possible outcomes, and use this table to determine 𝑃(7 ≤ total), 𝑃(no 4), and 𝑃(red die > blue die)
b) Five average dice are rolled together, use the binomial probability formula to determine the probability that exactly three of the dice will show a 4. - A hand of four cards is dealt from a standard deck. Determine the probability that;
a) Such a hand contains only court cards (i.e. J, Q, or K)?
b) All four cards in a hand are of the same suit?
c) All four cards in a hand are of different suits?
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