Mathematics 10 — Exercise 12.1 · Q8 (i)

Full question

A bag contains 4 red, 5 white, 6 green and 3 black balls. One ball is drawn at random. Find the probability that it is white.

Step-by-step solution

1. Count all balls for the denominator and all eligible colours for the numerator.

2. Substitute the given probabilities or outcome counts.

   $$\frac{5}{4+5+6+3}$$

3. Calculate this operation before combining the remaining terms.

   $$4+5+6+3=18$$

4. Calculate this operation before combining the remaining terms.

   $$5\times 1=5$$

5. Calculate this operation before combining the remaining terms.

   $$1\times 18=18$$

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

   $$\frac{5\times 1}{1\times 18}$$

7. Calculate these two products separately.

   $$\frac{5}{18}$$

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

   $$\frac{1\times 1}{1\times 18}$$

9. Calculate these two products separately.

   $$\frac{1}{18}$$

10. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{18}=\frac{1}{18}$$

11. Calculate this operation before combining the remaining terms.

    $$5\times \frac{1}{18}=\frac{5}{18}$$

12. The simplified result is the required probability.

    $$\frac{5}{18}$$

Answer

The final answer is shown below.