A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see Fig. 15.5), and these are equally likely outcomes. What is the probability that it will point at

(i) 8?
(ii) an odd number?
(iii) a number greater than 2?
(iv) a number less than 9?

Total number of possible outcomes = 8

\( P(E) \ = \ \frac{Number \ of \ favourable \ outcomes}{Total \ number \ of \ outcomes} \)

(i) Total number of favourable events (i.e. 8) = 1

P(pointing at 8) \( = \ \frac{1}{8} \ = \ 0.125 \)

(ii) Total number of odd numbers = 4 (1, 3, 5 and 7)

P(pointing at an odd number) \( = \ \frac{4}{8} \ = \ 0.5 \)

(iii) Total numbers greater than 2 = 6 (3, 4, 5, 6, 7 and 8)

P(pointing at a number greater than 4) \( = \ \frac{6}{8} \ = \ 0.75 \)

(iv) Total numbers less than 9 = 8 (1, 2, 3, 4, 5, 6, 7, and 8)

P(pointing at a number less than 9) \( = \ \frac{8}{8} \ = \ 1 \)