Mathematics 10 — Exercise 12.1 · Q4

Full question

A coin is tossed three times. Find the probability of getting two consecutive 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.

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

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.

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

13. Consecutive means adjacent tosses: TTH,HTT and TTT qualify. If the intention were exactly two tails, TTT would be excluded; the question does not say exactly.

14. The printed answer key gives 1/4, interpreting the question as EXACTLY two tails that are adjacent. Its favourable outcomes are HTT and TTH, so2/8=1/4. If TTT is also allowed, the answer is3/8.

Answer

Textbook interpretation (exactly two consecutive tails):1/4. At least two consecutive tails:3/8.