Mathematics 10 — Exercise 12.1 · Q7 (iv)

Full question

Three fair coins are tossed. Find the probability of obtaining exactly two heads.

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.

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

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

   $$\frac{3}{8}$$

4. Calculate this operation before combining the remaining terms.

   $$3\times 1=3$$

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.

   $$\frac{3\times 1}{1\times 8}$$

7. Calculate these two products separately.

   $$\frac{3}{8}$$

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

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

9. Calculate these two products separately.

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

10. Calculate this operation before combining the remaining terms.

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

11. Calculate this operation before combining the remaining terms.

    $$3\times \frac{1}{8}=\frac{3}{8}$$

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

    $$\frac{3}{8}$$

Answer

The final answer is shown below.