The probability that a woman of age 40 has breast cancer is about 1 percent. Which Team Will Win? Given that an athlete is not taking the banned substance, what is the probability that they test positive? What do you think about the test – how effective is it? 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. Unfortunately, he also accuses some students who are telling the truth. How would this change the expected results? What are the different ways of getting a draw? 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.

Register for our mailing list. 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.

# Who Is Cheating? :

Does this mean they will always win? Think of women.

Age 11 to 14 Challenge Level: What do you think about the test – how effective is it? The Dog Ate My Homework!

But if conditional probability is about the chance that a positive test for cancer means you actually have cancer – that matters. Display a large tree diagram, with the expected results for 36 trials, and a second blank tree diagram.

In addition, they will become more aware of the need for care in deciding which data subset provides homewkrk figure nrichh the denominator of a probability. Register for our mailing list. Display this on the first set of branches of the second tree diagram.

# The Dog Ate My Homework! :

Rather than drawing attention to this, give students a chance to observe that the game “isn’t fair”, and use this to discuss that perhaps Team Yeti are a much stronger team What proportion would we expect them to win?

How could you improve it, to make it more realistic? The approach used in this problem will help to structure their understanding of the questions that can be answered from tree diagrams and 2-way tables, and will lead them to the multiplication rule. A new test is in development to try to identify athletes who use a certain banned substance to enhance their performance.

Put students into groups of 3 or 4, and have each group collect the equipment they need. Is the proportion of games won by the Yetis Beavers the same as the probability that they will score a goal?

The game is deliberately set up so that Team Yeti are more likely to score than Team Beaver. When everyone has collected their data, get all groups to record their data on the worksheetand then put their pairs of cubes on a large tree diagram or 2-way table.

homeworrk

This Sample Space worksheet will help students to identify correctly all the possible outcomes, and to see how many give the required result. Are you surprised by the results? 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.

## Great Expectations

Which Team Will Win? Can we simplify that? A practical experiment which will introduce students to tree diagrams, and help them to understand that outcomes may not be equally likely.

For many students, conditional probability seems to be too hard, and pointless anyway. In each question, the numerator is therefore 3.

## Conditional Probability Is Important for All Students!

If she has breast cancer, the probability that she tests positive on a screening mammogram is 90 percent. 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.

Group the students into threes as far as possible. Then get them to collect data – pairs of multi-link cubes – for 36 athletes. What are the different ways of getting a draw? Given that an athlete is taking the banned substance, what is the probability that the test is negative?