Spots and measles
99% of people who have measles have spots. Ben has spots. Do you think he has measles?
Age
11 to 16
Challenge level
Problem
This resource is part of the collection Probability and Evidence.
99% of people who have measles have spots. If Ben has red spots, how likely do you think it is it that he has measles?
Here are three pieces of information that might help you to work out this probability:
- There are about 12 million children in the UK.
- About 1,200 of these get measles every year.
- Roughly 10% of the 12 million children suffer from spots.
How might you be able to use this information to be able to calculate the probability that Ben has measles?
Are there any tables or diagrams that might help you represent this information?
Click below to see a possible method for organising the information:
You could draw a two-way (or contingency) table like this.
| Measles | Not Measles | Total | |
|---|---|---|---|
| Spots | |||
| No Spots | |||
| Total | 12 000 000 |
Can you use the information to complete the table?
Can you now work out the probability that Ben has measles?
Are there any other factors that might affect the probability that Ben has measles?
How could you factor these into the calculations?
Student Solutions
Well done to students from Garden International School in Malaysia who used a two-way table to organise the data. Keishiro wrote up her answer neatly and Daigo showed his working out.
Zach wrote up his findings in a very clear way. He also thought about other factors that could affect the probability.
Thank you to everyone who submitted a solution.