Sets 3
4 marks · Normal54 children were surveyed about their favourite types of fruit. The Venn diagram below shows the number of children who like oranges (O), bananas (B), and apples (A).
| Region | No. of children |
|---|---|
| O only | 10 |
| B only | 8 |
| A only | 7 |
| O and B only | 6 |
| B and A only | 5 |
| O and A only | 4 |
| All three fruits | 9 |
| None of these fruits | ? |
Complete the table by finding the number of children who do not like any of these three fruits. Then, using the information, find the probability that a randomly selected child from this group likes at least two of the three fruits.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
Must show: 'None of these fruits' = 5, 'Likes at least two fruits' = 24/54 or 4/9
Also accept: Probability as 0.444; 24/54
Common mistakes: Wrong sum or omitting the 'all three' region when counting overlaps
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Sums all regions except for 'none', subtracts from total to find children who chose none. (follow-through)
A1 · 1 mark · Correctly completes: 'None of these fruits' = 5.
M2 · 1 mark · Correctly adds up all regions representing at least two fruits.
A2 · 1 mark · Gives probability as 24/54, 4/9, or decimal equivalent.
Worked solution
Sum all regions: 10 + 8 + 7 + 6 + 5 + 4 + 9 = 49.
None = 54 - 49 = 5.
| Region | No. of children |
|---|---|
| O only | 10 |
| B only | 8 |
| A only | 7 |
| O and B only | 6 |
| B and A only | 5 |
| O and A only | 4 |
| All three fruits | 9 |
| None of these fruits | 5 |
At least two fruits: O and B only (6) + B and A only (5) + O and A only (4) + All three (9) = 6 + 5 + 4 + 9 = 24.