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Ali (A), Blake (B), Rowan (R) and Sam (S) are in a relay team - OCR - GCSE Maths - Question 11 - 2021 - Paper 1
Question 11
Ali (A), Blake (B), Rowan (R) and Sam (S) are in a relay team. Sam always runs fourth in the team. The order for the other three is chosen at random. (a) Complete t... show full transcript
Worked Solution & Example Answer:Ali (A), Blake (B), Rowan (R) and Sam (S) are in a relay team - OCR - GCSE Maths - Question 11 - 2021 - Paper 1
Step 1
Complete this table to show all the possible orders for the team.
Answer
To complete the table with the possible team orders of Ali (A), Blake (B), and Rowan (R) while Sam (S) runs fourth, we need to enumerate all the permutations of the first three positions. There are 3 runners (A, B, R) that can be arranged in various ways:
- Row 1: A, B, R, S
- Row 2: A, R, B, S
- Row 3: B, A, R, S
- Row 4: B, R, A, S
- Row 5: R, A, B, S
- Row 6: R, B, A, S
Thus, the completed table is:
| First | Second | Third | Fourth |
|---|---|---|---|
| A | B | R | S |
| A | R | B | S |
| B | A | R | S |
| B | R | A | S |
| R | A | B | S |
| R | B | A | S |
Step 2
Find the probability that Ali will run first.
Answer
To find the probability that Ali will run first, we observe that there are a total of 6 possible ways (as calculated in part (a)) to arrange the team.
Only one of these arrangements will have Ali in the first position. Therefore, the probability can be calculated as follows:
Thus, the probability that Ali will run first is ( \frac{1}{6} ).