Mathematics 10 — Exercise 12.1 · Q9 (i)

Full question

One integer is selected at random from the integers 1 to 15 inclusive, all with equal probability. Find the probability of selecting an odd number.

Step-by-step solution

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

   $$\mathrm{n(S)}=15$$

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

   $$\mathrm{n(E)}=8$$

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

   $$\frac{8}{15}$$

4. Calculate this operation before combining the remaining terms.

   $$8\times 1=8$$

5. Calculate this operation before combining the remaining terms.

   $$1\times 15=15$$

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

   $$\frac{8\times 1}{1\times 15}$$

7. Calculate these two products separately.

   $$\frac{8}{15}$$

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

   $$\frac{1\times 1}{1\times 15}$$

9. Calculate these two products separately.

   $$\frac{1}{15}$$

10. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{15}=\frac{1}{15}$$

11. Calculate this operation before combining the remaining terms.

    $$8\times \frac{1}{15}=\frac{8}{15}$$

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

    $$\frac{8}{15}$$

Answer

The final answer is shown below.