9-11 State Maths Paper 2021. docx

QUESTION THREE
LUCK OF THE DRAW
16 MARKS
Everyone dreams of winning the
lottery, however, the odds are stacked against us. This question will reveal just how
unlikely a lottery win actually is.
QUESTION ONE (4 MARKS)
A standard lottery sees 6 numbers drawn in a row, from a pool of balls numbered 1 to 49, without replacement. Calculate the chance of
winning this lottery (i.e. of picking the 6 numbers in any order.
QUESTION TWO (4 MARKS)
Now, calculate the chance of picking just
one correct number

Task developed by Giacomo Rotolo-Ross, University of Sydney, 2020
7
QUESTION THREE (2 MARKS)
How about the chance of coming oh so close and picking
five correct numbers

Task developed by Giacomo Rotolo-Ross, University of Sydney, 2020
8
QUESTION FOUR (SIX MARKS)
Below are details for six types of lotteries across the world – order them from
most to least
likely to be won.
•
Irish Lotto – 6 numbers, 47 balls
•
PowerBall – 5 numbers plus 1 bonus number, 69 balls plus 26 bonus balls
•
MegaMillions – 5 numbers plus 1 bonus number, 70 balls plus 25 bonus balls
•
EuroJackpot – 5 numbers plus 2 bonus numbers, 50 balls plus 10 bonus balls
•
Oz Lotto – 7 numbers, 45 balls
•
EuroMillions - 5 numbers plus 2 bonus numbers, 50 balls plus 12 bonus balls
Answers:
1. _______________________________________ (most likely to be won)
2. _______________________________________
3. _______________________________________
4. _______________________________________
5. _______________________________________
6. _______________________________________ (least likely to be won)

Task developed by Giacomo Rotolo-Ross, University of Sydney, 2020
9
QUESTION FOUR
SIGNING OFF
9 MARKS
Probability involves a significant number of
mathematical signs and symbols, many of which are rarely seen in any other fields. Are you able to
draw those named in the table below (some, but not all of which, are probability-related)?
SIGN OR SYMBOL NAME
ANSWER (DRAWING)
Summation is proportional to Real numbers because Population mean Standard deviation Combination Permutation Delta
END OF PAPER