Jacob, Amelie and Reuben each roll a fair six-sided dice - OCR - GCSE Maths - Question 3 - 2019 - Paper 1

To solve for the probability that all three players roll a number less than 3, we first identify the favorable outcomes for a single roll of a six-sided die.

The numbers less than 3 on a six-sided die are 1 and 2. Thus, the favorable outcomes are:

• 1
• 2

Therefore, there are 2 favorable outcomes. The total number of outcomes when rolling a six-sided die is 6.

The probability of one person rolling a number less than 3 is:

$P( ext{less than 3}) = \frac{2}{6} = \frac{1}{3}$

Since Jacob, Amelie, and Reuben roll their dice independently, the joint probability that all three roll less than 3 is given by the product of their individual probabilities:

$P( ext{all less than 3}) = P( ext{less than 3}) \times P( ext{less than 3}) \times P( ext{less than 3}) = \left(\frac{1}{3}\right)^3 = \frac{1}{27}$

Therefore, the final answer, expressed as a fraction in its simplest form, is:

$\frac{1}{27}$