Bart and Bethany play a game. They each roll a regular 6-sided die labeled 1to 6. Use an outcome table to show all possible outcomes: (2 marks) is the total number of outcomes 12?
To determine all possible outcomes when rolling two regular 6-sided dice, we can create an outcome table.
The outcome table shows the possible values for the rolls of the two dice, considering each die individually. We then take all possible combinations of the values and list them in the table.
Here is the outcome table:
| | Die 1 | Die 2 |
|---|-------|-------|
| 1 | 1 | 1 |
| 2 | 1 | 2 |
| 3 | 1 | 3 |
| 4 | 1 | 4 |
| 5 | 1 | 5 |
| 6 | 1 | 6 |
| 7 | 2 | 1 |
| 8 | 2 | 2 |
| 9 | 2 | 3 |
| 10 | 2 | 4 |
| 11 | 2 | 5 |
| 12 | 2 | 6 |
| 13 | 3 | 1 |
| 14 | 3 | 2 |
| 15 | 3 | 3 |
| 16 | 3 | 4 |
| 17 | 3 | 5 |
| 18 | 3 | 6 |
| 19 | 4 | 1 |
| 20 | 4 | 2 |
| 21 | 4 | 3 |
| 22 | 4 | 4 |
| 23 | 4 | 5 |
| 24 | 4 | 6 |
| 25 | 5 | 1 |
| 26 | 5 | 2 |
| 27 | 5 | 3 |
| 28 | 5 | 4 |
| 29 | 5 | 5 |
| 30 | 5 | 6 |
| 31 | 6 | 1 |
| 32 | 6 | 2 |
| 33 | 6 | 3 |
| 34 | 6 | 4 |
| 35 | 6 | 5 |
| 36 | 6 | 6 |
From the outcome table, we can see that there are 36 possible outcomes when rolling two regular 6-sided dice. Therefore, the total number of outcomes is 36, not 12.
To create an outcome table, we can list all the possible outcomes by considering the numbers each player can roll on the die.
Bart's roll possibilities: 1, 2, 3, 4, 5, 6
Bethany's roll possibilities: 1, 2, 3, 4, 5, 6
Now, we can list all the possible outcomes by combining Bart's and Bethany's rolls:
Bart: 1, Bethany: 1
Bart: 1, Bethany: 2
Bart: 1, Bethany: 3
Bart: 1, Bethany: 4
Bart: 1, Bethany: 5
Bart: 1, Bethany: 6
Bart: 2, Bethany: 1
Bart: 2, Bethany: 2
Bart: 2, Bethany: 3
Bart: 2, Bethany: 4
Bart: 2, Bethany: 5
Bart: 2, Bethany: 6
Bart: 3, Bethany: 1
Bart: 3, Bethany: 2
Bart: 3, Bethany: 3
Bart: 3, Bethany: 4
Bart: 3, Bethany: 5
Bart: 3, Bethany: 6
Bart: 4, Bethany: 1
Bart: 4, Bethany: 2
Bart: 4, Bethany: 3
Bart: 4, Bethany: 4
Bart: 4, Bethany: 5
Bart: 4, Bethany: 6
Bart: 5, Bethany: 1
Bart: 5, Bethany: 2
Bart: 5, Bethany: 3
Bart: 5, Bethany: 4
Bart: 5, Bethany: 5
Bart: 5, Bethany: 6
Bart: 6, Bethany: 1
Bart: 6, Bethany: 2
Bart: 6, Bethany: 3
Bart: 6, Bethany: 4
Bart: 6, Bethany: 5
Bart: 6, Bethany: 6
By listing all the possible outcomes, we can see that there are a total of 36 outcomes (6 possibilities for Bart's roll and 6 possibilities for Bethany's roll). Therefore, the total number of outcomes is 36, not 12.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
6 * 6 = ?