Two Dice Game I
For each dice game below (Game A and Game B) you are to:
· decide if each game is fair or not and explain your answer (parts a) and b));
· play Game A and Game B in pairs, but individually record and explain your results (parts c) and d)).
Game A: Throw the two dice and add the top two numbers together.
· Player 1 wins when the result is an odd number.
· Player 2 wins when the result is an even number.
|
Sum = 6
|
a) i) Using the table below, who is more likely to win this game? (Circle one)
(A) Player 1 (B) Player 2 (C) Both players are equally likely.
ii) Explain your answer.
Player 2 would win because there are more even numbers on the table than there are odd numbers. There are 3, 5, 7, 9 and 11 which are odd numbers and then there are 2, 4, 6, 8, 10 and 12 which are even. So there is a more of a chance rolling even numbers.
| Sum of two dice |
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Number of ways it can occur |
1
|
2
|
3
|
4
|
5
|
6
|
5
|
4
|
3
|
2
|
1
|
Game B: Throw the two dice and multiply the top two numbers together.
· Player 1 wins when the result is an odd number.
· Player 2 wins when the result is an even number.
|
Product = 8
|
b) i) Who is more likely to win this game? (Circle one)
(A) Player 1 (B) Player 2 (C) Both players are equally likely.
ii) Explain your answer.
Both players are equally likely to win because there is a fifty fifty chance of getting an odd or an even number when multiplying the top two numbers.
· Pair up with someone else who has finished a) and b).
· Get two dice and complete parts c) and d).
|
c) i) Play Game A 50 times and record your results in the table below.
Tally
|
Frequency
|
| Player 1 wins | IIIII IIIII IIIII IIIII IIIII I | O.26 |
| Player 2 wins | IIIII IIIII IIIII IIIII IIII | O.24 |
ii) Do your results suggest that Game A is fair? Yes / No (Circle one)
Explain your answer.
Yes because player 1 had 26 and player 2 had 24 which means both of the players almost got 25 each which is half of fifty.
d) i) Play Game B 50 times and record your results in the table below.
Tally
|
Frequency
|
| Player 1 wins | IIIII IIIII III | O.13 |
| Player 2 wins | IIIII IIIII IIIII IIIII IIIII IIIII IIIII II | O.37 |
ii) Do your results suggest that Game B is fair? Yes / No (Circle one)
Explain your answer.
Game b is not fair because player 2 got more wins than player 1. Player 2 got 37 , player 1 got 13 so this proves that game b is not fair.
