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Jacob, Amelie and Reuben each roll a fair six-sided dice - OCR - GCSE Maths - Question 21 - 2019 - Paper 1

Question 21

Jacob, Amelie and Reuben each roll a fair six-sided dice. What is the probability that all three roll a number less than 3? Give your answer as a fraction in its si... show full transcript

Worked Solution & Example Answer:Jacob, Amelie and Reuben each roll a fair six-sided dice - OCR - GCSE Maths - Question 21 - 2019 - Paper 1

Step 1

Calculate individual probabilities

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Answer

On a fair six-sided die, the numbers less than 3 are 1 and 2. Thus, there are 2 favorable outcomes out of 6 possible outcomes. The probability for one person to roll a number less than 3 is:

$P(<3) = \frac{2}{6} = \frac{1}{3}$

Step 2

Calculate the probability for all three

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Answer

Since Jacob, Amelie, and Reuben roll independently, we multiply their probabilities:

$P(all <3) = P(Jacob <3) \times P(Amelie <3) \times P(Reuben <3)$

Substituting the individual probabilities:

$P(all <3) = \left(\frac{1}{3}\right) \times \left(\frac{1}{3}\right) \times \left(\frac{1}{3}\right) = \frac{1}{27}$

Step 3

Final answer

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Answer

Thus, the probability that all three roll a number less than 3 is:

$P(all <3) = \frac{1}{27}$

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