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The table shows the relative frequencies of the results for a football team after a number of games - OCR - GCSE Maths - Question 5 - 2018 - Paper 1
Question 5
The table shows the relative frequencies of the results for a football team after a number of games. | Result of game | won | lost | drew | |------------------... show full transcript
Worked Solution & Example Answer:The table shows the relative frequencies of the results for a football team after a number of games - OCR - GCSE Maths - Question 5 - 2018 - Paper 1
Step 1
Complete the table.
Answer
To complete the table, we need to find the relative frequency of the 'drew' category. The sum of the relative frequencies for all outcomes should equal 1.
Let the relative frequency for 'drew' be denoted as . We can set up the following equation:
Solving for gives us:
Thus, the completed table will be:
| Result of game | won | lost | drew |
|---|---|---|---|
| Relative frequency | 0.2 | 0.45 | 0.35 |
Step 2
The team lost 10 more games than they won. How many games did the team play altogether?
Answer
Let represent the number of games won. According to the problem, the team lost 10 more games than they won, so we can denote the number of games lost as .
From the table, we know that the relative frequency of winning is 0.2. If the total number of games played is denoted as , we can express this relationship as:
ightarrow w = 0.2N$$ Similarly, the relative frequency for losing is 0.45: $$ rac{l}{N} = 0.45 ightarrow l = 0.45N$$ Now substituting $l$ from the first equation: $$0.45N = 0.2N + 10$$ Now simplify and solve for $N$: $$0.45N - 0.2N = 10$$ $$0.25N = 10$$ $$N = rac{10}{0.25} = 40$$ Therefore, the team played a total of **40 games**.