**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 **