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# 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) $$= \ \frac{8}{8} \ = \ 1$$