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GSCE Mathematics Problem Solving Handling Data Higher Tier

In a dice probability problem, we need to analyze the outcomes of rolling three dice: two black and one red, all numbered from 1 to 6. We must investigate the combinations where the total of the two black dice equals the score on the red die. By systematically working through all possible combinations, we can determine the probabilities associated with these outcomes. The question posed is whether each combination has the same probability and what the final probability is that the two black dice total the same as the red die after rolling.

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GSCE Mathematics Problem Solving Handling Data Higher Tier

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  1. GSCE Mathematics Problem Solving Handling Data Higher Tier

  2. Helping hand Write down the different combinations you could have – work systematically. Work out the probability of one of the combinations. Do all combinations have the same probability? Three dice are each numbered 1 to 6 Two of them are black and one is red. All three dice are rolled. What is the probability that the total on the two black dice will be equal to the score on the red dice?

  3. Answer The possible combinations are: 1 1 2 2 1 3 3 1 4 4 1 5 5 1 6 1 2 3 2 2 4 3 2 5 4 2 6 1 3 4 2 3 5 3 3 6 1 4 5 2 4 6 1 5 6 Each of these has probability 1 x 1 x 1 = 1 6 6 6 216 So for 15 combinations: 15 x 1 = 15 = 5 216 216 72 15 combinations

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