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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 for displaying outcomes when rolling two fair 6-sided dice because it can become overly complex. Specifically, the tree diagram would require many branches for each possible outcome, making it difficult to read and interpret, especially since there are a total of 36 outcomes.
Step 2
Draw a sample space to display all the possible outcomes.
Answer
The sample space for rolling two 6-sided dice can be represented in a table format or as a list. It consists of pairs of outcomes, where the first number represents the outcome of the first die and the second number represents the outcome of the second die. The sample space is as follows:
| Die 1 | Die 2 |
|---|---|
| (1,1) | (1,2) |
| (2,1) | (2,2) |
| (3,1) | (3,2) |
| (4,1) | (4,2) |
| (5,1) | (5,2) |
| (6,1) | (6,2) |
This sample space includes all 36 possible outcomes.
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 two dice adding to 11, we first identify the pairs that meet this condition:
The possible pairs are:
- (5,6)
- (6,5)
There are 2 favorable outcomes. Since there are a total of 36 possible outcomes when rolling two dice, the probability ( P ) can be calculated as:
Thus, the probability that the scores on the two dice add to 11 is indeed ( \frac{1}{18} ).