A game wheel is divided into three coloured sectors — Red (R), Blue (B) and Green (G). The wheel is spun 250 times during a school fair. The number of times the pointer stops at each colour is recorded below:
Colour Number of times stopped
R 73
B 82
G 96
On the basis of these observations, answer the following:
a. (i) Calculate the empirical probability of the pointer stopping at each colour.
b. (ii) Determine the total of the three probabilities obtained in part (i).
c. (iii) Obtain a corrected set of probabilities that preserves the relative proportions among R, B and G while making the total exactly 1. Give each corrected probability correct to three decimal places.
d. (iv) Verify that the corrected probabilities satisfy the non-negativity and normalisation properties of probability.