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21 people travelled to a meeting - OCR - GCSE Maths - Question 19 - 2019 - Paper 5
Question 19
21 people travelled to a meeting. - 12 used a train. - 6 used a car. - 7 did not use a train or a car. - Some used a train and a car. Two people are chosen at rand... show full transcript
Worked Solution & Example Answer:21 people travelled to a meeting - OCR - GCSE Maths - Question 19 - 2019 - Paper 5
Step 1
Step 2
Determine Overlap: People Who Used Both Train and Car
Answer
Let the number of people who used both a train and a car be denoted as 'x'. We already know that 6 people used a car. Therefore, those who used only a car would be (6 - x). Thus, the equation becomes:
Total using a train = Only persons using only a train + Those using both train and car
So, we get:
12 = (12 - x) + x
Solving for x, we can see that x must be an integer that fits within these constraints, knowing the other distribution of users.
Step 3
Calculate the Probability
Answer
The probability that both selected people used a car can be calculated with:
- First, find out how many people used only a car and how many did not use either.
- The total using a train is 12 and we derived 'x' earlier. Thus, the probability of selecting two people who used both train and car from those who used train can be computed by the combination formula:
Where C(n, r) is the combination of n items taken r at a time.
This will give us the final probability.