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. 14.5 ), 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?
Given:
- Numbers on the spinner: 1, 2, 3, 4, 5, 6, 7, 8
- Total outcomes = 8 (since there are 8 numbers)
(i) Probability that it points at 8:
- Favourable outcome = 1 (only the number 8)
Probability (8) = 1/8
(ii) Probability of an odd number:
- Odd numbers = 1, 3, 5, 7
- Favourable outcomes = 4
Probability (odd) = 4/8 = 1/2
(iii) Probability of a number greater than 2:
- Numbers greater than 2 = 3, 4, 5, 6, 7, 8
- Favourable outcomes = 6
Probability (>2) = 6/8 = 3/4
(iv) Probability of a number less than 9:
- All numbers (1 to 8) are less than 9
- Favourable outcomes = 8
Probability (<9) = 8/8 = 1