Handling Data 5
3 marks · NormalEmma spins a spinner twice, each time with probability 1/4 of landing on red and 3/4 of landing on blue. She draws a tree diagram to represent this. Explain, with reasoning, why the total probability for all possible outcomes is 1.
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The total probability for all possible outcomes is 1 because the tree diagram lists every possible pair of results (red or blue, each time), and the sum of the probabilities of all the branches must be 1, representing certainty that some outcome will occur.
Must show: States that all possible outcomes listed in tree diagram, Probabilities for all branches add to 1
Common mistakes: Do not reference the exhaustive nature of outcomes.
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Marking points
B1 · 1 mark · Mentions all possible outcomes are included in the tree diagram.
M1 · 1 mark · States that the sum of all probabilities for the branches is 1.
A1 · 1 mark · Explains this means that one of the outcomes must occur (certainty).
Worked solution
A tree diagram shows all possible outcomes: (Red, Red), (Red, Blue), (Blue, Red), (Blue, Blue).
Sum of probabilities: (1/4 × 1/4) + (1/4 × 3/4) + (3/4 × 1/4) + (3/4 × 3/4)
So, the tree diagram lists all outcomes and their probabilities sum to 1, representing certainty.