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Hannah wants to display all the possible outcomes when rolling two fair 6-sided dice - OCR - GCSE Maths - Question 8 - 2018 - Paper 1
Question 8
Hannah wants to display all the possible outcomes when rolling two fair 6-sided dice. (a) Give a reason why a tree diagram is not the best method to use. (b) (i) D... show full transcript
Worked Solution & Example Answer:Hannah wants to display all the possible outcomes when rolling two fair 6-sided dice - OCR - GCSE Maths - Question 8 - 2018 - Paper 1
Step 1
Give a reason why a tree diagram is not the best method to use.
Answer
A tree diagram is not the best method to use because it can become overly complicated and difficult to manage. Since there are a large number of possible outcomes when rolling two dice, specifically 36 outcomes, the tree would have too many branches, making it hard to read and understand.
Step 2
Draw a sample space to display all the possible outcomes.
Answer
The sample space can be represented in a table format, showing the outcomes of two six-sided dice:
| Die 1 \ Die 2 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | (1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) |
| 2 | (2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) |
| 3 | (3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) |
| 4 | (4,1) | (4,2) | (4,3) | (4,4) | (4,5) | (4,6) |
| 5 | (5,1) | (5,2) | (5,3) | (5,4) | (5,5) | (5,6) |
| 6 | (6,1) | (6,2) | (6,3) | (6,4) | (6,5) | (6,6) |
Step 3
Show that the probability of the scores on the two dice adding to 11 is \( \frac{1}{18} \).
Answer
To find the probability of the scores on the two dice adding up to 11, we first identify the pairs that yield this total:
- (5,6)
- (6,5)
There are a total of 2 favorable outcomes.
The total number of possible outcomes when rolling two dice is 36 (since each die has 6 faces, we have ( 6 \times 6 = 36 )).
Thus, the probability is: