Photo AI
Antonio rolls two fair six-sided dice and calculates the difference between the scores - OCR - GCSE Maths - Question 12 - 2019 - Paper 6
Question 12
Antonio rolls two fair six-sided dice and calculates the difference between the scores. For example, if the two scores are 2 and 5 or 5 and 2 then the difference is ... show full transcript
Worked Solution & Example Answer:Antonio rolls two fair six-sided dice and calculates the difference between the scores - OCR - GCSE Maths - Question 12 - 2019 - Paper 6
Step 1
Complete the sample space diagram to show the possible outcomes from Antonio's dice.
Answer
To complete the difference table, we need to calculate the difference between the outcomes from the two dice. The difference is calculated using the formula:
Here’s the filled-out table:
| Dice 2 \ Dice 1 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 2 | 3 | 4 | 5 |
| 2 | 1 | 0 | 1 | 2 | 3 | 4 |
| 3 | 2 | 1 | 0 | 1 | 2 | 3 |
| 4 | 3 | 2 | 1 | 0 | 1 | 2 |
| 5 | 4 | 3 | 2 | 1 | 0 | 1 |
| 6 | 5 | 4 | 3 | 2 | 1 | 0 |
Step 2
Calculate the probability that he gets a difference of 1 on all three rolls.
Answer
The possible differences of 1 occur when the outcome pairs are:
- (1, 2)
- (2, 1)
- (2, 3)
- (3, 2)
- (3, 4)
- (4, 3)
- (4, 5)
- (5, 4)
- (5, 6)
- (6, 5)
This gives us a total of 10 favorable outcomes for a difference of 1 in a single roll of the two dice. Since there are a total of 36 possible outcomes (6 sides on Dice 1 x 6 sides on Dice 2), the probability of getting a difference of 1 in one roll is
To find the probability of getting a difference of 1 on all three rolls, we calculate:
Thus, the final probability is ( \frac{125}{5832} ).