Mathematics 10 — Exercise 12.2 · Q7

Full question

A fair six-sided die is rolled twice. Find the probability of obtaining 3 at least once.

Step-by-step solution

1. All outcomes are equally likely. Count the complete sample space.

   $$\mathrm{n(S)}=36$$

2. Select exactly the outcomes satisfying the written condition. These are listed below.

   $$\mathrm{n(E)}=11$$

3. Probability=favourable outcomes / total equally likely outcomes.

   $$\frac{11}{36}$$

4. Calculate this operation before combining the remaining terms.

   $$11\times 1=11$$

5. Calculate this operation before combining the remaining terms.

   $$1\times 36=36$$

6. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{11\times 1}{1\times 36}$$

7. Calculate these two products separately.

   $$\frac{11}{36}$$

8. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{1\times 1}{1\times 36}$$

9. Calculate these two products separately.

   $$\frac{1}{36}$$

10. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{36}=\frac{1}{36}$$

11. Calculate this operation before combining the remaining terms.

    $$11\times \frac{1}{36}=\frac{11}{36}$$

12. Reduce the fraction by dividing numerator and denominator by their greatest common divisor.

    $$\frac{11}{36}$$

13. Count a3 on the first roll or the second, subtracting(3,3) once:6+6−1=11.

Answer

The final answer is shown below.