Mathematics 10 — Exercise 12.1 · Q9 (ii)

Full question

One integer is selected at random from the integers 1 to 15 inclusive, all with equal probability. Find the probability of selecting a multiple of 5.

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.

   $$\mathrm{n(E)}=3$$

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

   $$\frac{3}{15}$$

4. Calculate this operation before combining the remaining terms.

   $$3\times 1=3$$

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.

   $$\frac{3\times 1}{1\times 15}$$

7. Calculate these two products separately.

   $$\frac{3}{15}$$

8. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

   $$\mathrm{GCD}=3$$

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

   $$\frac{3\times 1}{1\times 3}$$

10. Calculate these two products separately.

    $$\frac{3}{3}$$

11. Show the two divisions explicitly.

    $$\frac{\frac{3}{3}}{\frac{3}{3}}$$

12. Write the reduced fraction.

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

13. Calculate this operation before combining the remaining terms.

    $$3\times \frac{1}{3}=1$$

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

    $$\frac{15\times 1}{1\times 3}$$

15. Calculate these two products separately.

    $$\frac{15}{3}$$

16. Show the two divisions explicitly.

    $$\frac{\frac{15}{3}}{\frac{3}{3}}$$

17. Write the reduced fraction.

    $$5\times \frac{1}{1}$$

18. Calculate this operation before combining the remaining terms.

    $$15\times \frac{1}{3}=5$$

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

    $$\frac{1\times 1}{1\times 5}$$

20. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{5}=\frac{1}{5}$$

21. Show the two divisions explicitly.

    $$\frac{\frac{3}{3}}{\frac{15}{3}}$$

22. Evaluate the numerator division.

    $$\frac{3}{3}=1$$

23. Evaluate the denominator division.

    $$\frac{15}{3}=5$$

24. Write the reduced fraction.

    $$\frac{1}{5}$$

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

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

26. Calculate these two products separately.

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

27. Calculate this operation before combining the remaining terms.

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

28. Calculate this operation before combining the remaining terms.

    $$3\times \frac{1}{15}=\frac{1}{5}$$

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

    $$\frac{1}{5}$$

Answer

The final answer is shown below.