Mathematics 10 — Exercise 12.1 · Q7 (i)

Full question

Three fair coins are tossed. Find the probability of obtaining three tails.

Step-by-step solution

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

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

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

   $$\mathrm{n(E)}=1$$

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

   $$\frac{1}{8}$$

4. Calculate this operation before combining the remaining terms.

   $$1\times 1=1$$

5. Calculate this operation before combining the remaining terms.

   $$1\times 8=8$$

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

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

7. Calculate these two products separately.

   $$\frac{1}{8}$$

8. Calculate this operation before combining the remaining terms.

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

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

   $$\frac{1}{8}$$

Answer

The final answer is shown below.