Transition Year Maths
9. Using the digits 1 and 2 only, how many different 3-digit numbers can you make? Find the probability of one being the number 121.
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10. Using the digits 4 and 5 only, how many different 4-digit numbers can you make? Pick one of these numbers at random. What are the chances it has exactly two 5’s in it?
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3-DOOR GAME SHOW PROBLEM
Yes, she should change her mind because by doing so she increases her chance of winning the car! If she sticks to her original choice of door she has a 1 in 3 chance of winning the car and there is a 2 in 3 chance that the car is behind one of the two other doors.
When the host opens one of those two other doors the 2 in 3 chance of the car being behind one of those two doors does not change so the 2 in 3 chance now applies to the unopened door. Therefore by changing she has a 2 in 3 chance of winning the car.
‘The Golf Bet’ Solution Golf Bet Project
He will owe €131,072. After hole one he owes €1, then €2, the €4 then €8 etc. The answer can also be got from 217 term of the sequence 1, 2, 4, 8, 16, 32 ... is 217 In general: the nth
. The 18th = 131,072. term of the sequence 1, 2, 4, 8, 16, 32 ... = 2n-1
104
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