Mathematics 10 — Exercise 12.2 · Q2

Full question

One house number is selected at random from the numbers 1 to 50 inclusive. Find the probability that the number is even or a perfect square.

Step-by-step solution

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

   $$\mathrm{n(S)}=50$$

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

   $$\mathrm{n(E)}=29$$

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

   $$\frac{29}{50}$$

4. Calculate this operation before combining the remaining terms.

   $$29\times 1=29$$

5. Calculate this operation before combining the remaining terms.

   $$1\times 50=50$$

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

   $$\frac{29\times 1}{1\times 50}$$

7. Calculate these two products separately.

   $$\frac{29}{50}$$

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

   $$\frac{1\times 1}{1\times 50}$$

9. Calculate these two products separately.

   $$\frac{1}{50}$$

10. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{50}=\frac{1}{50}$$

11. Calculate this operation before combining the remaining terms.

    $$29\times \frac{1}{50}=\frac{29}{50}$$

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

    $$\frac{29}{50}$$

13. Squares are 1,4,9,16,25,36,49. Even squares 4,16,36 overlap:25+7−3=29 favourable numbers.

Answer

The final answer is shown below.