Worked example 2 Aisling is at a carnival and sees a game which involves a spinner.
The spinner she will play is shown. The game seems fair, so Aisling decides to play.
(i) Looking at the spinner, what is the probability of Aisling (a) winning (b) losing?
(ii) Do you think Aisling was right to assume this is a fair game?
(iii) Aisling plays the game fi ve times and does not win at all. Aisling thinks the game is biased. Is she correct? Justify your answer.
(iv) Aisling doesn’t play anymore games, but she watches 40 other people play the game and only 5 people win a prize. She is now convinced the game is biased. Is she correct? Justify your answer.
Solution (a)
(ii) (iii) (iv)
Releative frequency = the total number of trials
____________________ number of successful trials
Worked example 3 Each of the graphs provided show the results after a single six-sided die has been rolled a number of times.
Graph 1 40
10 20 30
Total rolls = 10 Graph 2 40
1 1
2 2
3 4
4 1
Graph 3 2 000
5 00 1 000 1 500
1 2 3 4 5 6
For each graph: (i) State the theoretical probability of any number between 1 and 6 being rolled. (ii) Find the missing values A, B, and C in the frequency tables on the next page. (iii) State if you think the die is fair, biased, or if there is not enough information to tell. Justify your answer. (iv) State what you notice about the sum of all the relative frequencies.