Handling Data 7
2 marks · EasyA bag contains 1 red, 2 blue and 3 green counters. You take one at random, replace it, and then take a second counter at random. Explain why a tree diagram can be used to represent all possible outcomes for this problem.
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Must show: Events are independent, All possible outcomes can be shown, Probabilities remain the same for each draw
Also accept: The draws are independent and replacing the counter keeps the probabilities the same, so all possible outcomes can be shown in a tree diagram.
Common mistakes: Saying events are dependent; Not mentioning replacement
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Marking points
B1 · 1 mark · States the events are independent due to replacement
B2 · 1 mark · Explains a tree diagram can show all possible outcomes for both draws
Worked solution
Since after each draw the counter is replaced, the probability of choosing each colour stays the same. The events are independent. A tree diagram can show every possible outcome for both draws and their probabilities.