Mathematics 10 — Exercise 12.2 · Q11

Full question

Two fair coins are tossed. Find the probability of obtaining two heads or two tails.

Step-by-step solution

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

   $$\mathrm{n(S)}=4$$

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

   $$\mathrm{n(E)}=2$$

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

   $$\frac{2}{4}$$

4. Calculate this operation before combining the remaining terms.

   $$2\times 1=2$$

5. Calculate this operation before combining the remaining terms.

   $$1\times 4=4$$

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

   $$\frac{2\times 1}{1\times 4}$$

7. Calculate these two products separately.

   $$\frac{2}{4}$$

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

   $$\mathrm{GCD}=2$$

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

   $$\frac{2\times 1}{1\times 2}$$

10. Calculate these two products separately.

    $$\frac{2}{2}$$

11. Show the two divisions explicitly.

    $$\frac{\frac{2}{2}}{\frac{2}{2}}$$

12. Write the reduced fraction.

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

13. Calculate this operation before combining the remaining terms.

    $$2\times \frac{1}{2}=1$$

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

    $$\frac{4\times 1}{1\times 2}$$

15. Calculate these two products separately.

    $$\frac{4}{2}$$

16. Show the two divisions explicitly.

    $$\frac{\frac{4}{2}}{\frac{2}{2}}$$

17. Write the reduced fraction.

    $$2\times \frac{1}{1}$$

18. Calculate this operation before combining the remaining terms.

    $$4\times \frac{1}{2}=2$$

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

    $$\frac{1\times 1}{1\times 2}$$

20. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{2}=\frac{1}{2}$$

21. Show the two divisions explicitly.

    $$\frac{\frac{2}{2}}{\frac{4}{2}}$$

22. Evaluate the numerator division.

    $$\frac{2}{2}=1$$

23. Evaluate the denominator division.

    $$\frac{4}{2}=2$$

24. Write the reduced fraction.

    $$\frac{1}{2}$$

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

    $$\frac{1\times 1}{1\times 4}$$

26. Calculate these two products separately.

    $$\frac{1}{4}$$

27. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{4}=\frac{1}{4}$$

28. Calculate this operation before combining the remaining terms.

    $$2\times \frac{1}{4}=\frac{1}{2}$$

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

    $$\frac{1}{2}$$

Answer

The final answer is shown below.