What’s the fairest way to choose 2 from 8 potential prize winners? All of this is by way of saying that it is vital that students – all students, not just the higher achieving groups who will do higher level exams – need to be helped to understand conditional probability. Over a week season, which team is likely to win more games? The denominator in each case is different, however, since we are considering these 3 athletes as a proportion of a different set of athletes in each case. On the tree diagram with the expected results, ask students what proportion of the 36 trials would result in each outcome, and show these figures on the right hand ends of the branches. But if conditional probability is about the chance that a positive test for cancer means you actually have cancer – that matters.

Register for our mailing list. Otherwise, groups should be provided with one normal die – in this case 1, 2, 3 and 4 correspond to a yellow face, and 5, 6 to a blue face. When everyone has collected their data, get all groups to record their data on the worksheet , and then put their pairs of cubes on a large tree diagram or 2-way table. A practical experiment which uses tree diagrams to help students understand the nature of questions in conditional probability. Are you surprised by the results?

What proportion would we expect them to win? To support this aim, members of the NRICH team nrlch in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. Age 14 to 16 Challenge Level: That wouldn’t matter if it were purely a mathematical problem, but failing to understand information given in this way is at the root of many medical and legal miscalculations.

To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

The Dog Ate My Homework!

One has breast cancer, and she will probably test positive. Given that an athlete is not taking the banned substance, what is the probability that they test positive? Unfortunately, he also accuses some students who are telling the truth.

What are the chances that a woman who tests positive actually has breast cancer? If that’s how it’s taught, then yes, it is dry, apparently pointless, and difficult to justify spending time and effort on.

# The ELISA Test :

Display a large tree diagram, with the expected results for 36 trials, and a second blank tree diagram. Considering just the drawswho scored first most often? For many students, conditional probability seems to be too hard, and pointless anyway. But if conditional probability is about the chance that a positive test for cancer means you actually have cancer – that matters.

His results are alarming. How likely are you to be chosen?

There are also questions which will help them to examine what happened compared to what we would expect to happen. What assumptions does it make?

## Great Expectations

All of this is by way of saying that it is vital that students – all students, not just the higher achieving groups who will do higher level exams – need to be helped to understand conditional probability. For nroch second sets of branches, focus on the proportion of the 24 or 12 athletes who would test positive and negative. The probability that a woman of age 40 has breast cancer is about 1 percent. Age 11 to 16 Challenge Level: To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

We believe that our problems provide students with contexts and structure which will enable them to do this:.

Which team will win? It is designed for classroom use; see the Teachers’ Resources for a suggested classroom approach. A practical experiment which uses tree diagrams to help students understand the nature of questions in conditional probability. If she does not have breast cancer, the probability that she nevertheless tests positive is 9 percent.

The denominator in each case is different, however, since we are considering these 3 athletes as a proportion of a different set of athletes in each case.

How could you improve it, to make it more realistic? Explain the scenario, and ask each group to throw their die, to simulate one football game.

Then get them to collect data – pairs of multi-link cubes – for 36 athletes. Is the proportion of games won by the Yetis Beavers the same as the probability that they will score a goal? Age 11 to 14 Challenge Level: