## Exam-Style Question on Sets## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 99. This question is similar to one that appeared on an IB Studies paper in 2014. The use of a calculator is allowed.

Twenty nine children went to a zoo to photograph some animals. The numbers of children who photographed Lions(L), Monkeys(M) and Zebras (Z) are given as follows:

- 6 of the children photographed all three
- 9 photographed Lions and Zebras
- 2 photographed Monkeys and Lions but not Zebras
- 3 photographed Lions only
- 4 photographed Monkeys only
- 10 photographed Zebras only

(a) Draw a Venn diagram to show this information.

All of the children photographed at least one of the three types of animal.

(b) Find the number of children that photographed Monkeys and Zebras but not Lions.

(c) Calculate the probability that a child chosen at random from the group photographed a Lion.

(d) Calculate the probability that a child chosen at random from the group photographed only one of the three types of animal.

(e) Calculate the probability that a child chosen at random from the group photographed only Lions, given that they saw only one of the three types of animal.

(f) If a child chosen at random from the group photographed the Lions, find the probability that they also photographed the Monkeys.

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