23.5 Venn diagrams and set notation — Practise with help
Work each question first. Open the hint if you need it, then reveal the working to check.
Warm-up: remember
Try these from memory before opening the answers.
- Work out .
- What does “both” mean in a group diagram?
Check
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- The overlap.
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Practise with help
1. In a group of 25, 14 like tea, 11 like coffee and 6 like both. How many like neither?
Hint
Subtract the overlap from each set before adding the exclusive regions.
Full working
Tea only is 8; coffee only is 5; both is 6. So 19 like at least one, and like neither.
2. A fair six-sided die is rolled. Find the probability of a result less than 3.
Hint
List the die results that meet the condition, then divide by six.
Full working
The matching results are 1 and 2, so the probability is .
3. Write in words what means.
Hint
Count the results less than 3, then divide by the six equally likely die results.
Full working
In both A and B.