A box contains 5 red marbles, 8 white marbles, and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red? (ii) white? (iii) not green?

Step 1: Find the possible out comes of an event
NOTE: Saying that a marble is drawn at random means all the marbles are equally likely to be drawn.
Therefore, the number of possible outcomes = 5 + 8 + 4 = 17
Let R denote the event 'marble is red
W denote the event 'the marble is white',
G denote the event 'the marble is green'
Step 2: Determine the number of outcomes favourable to the event
(i) Number of red marbles = 5
The number of outcomes favourable to the R = 5
(ii) Number of white marbles = 8
The number of outcomes favourable to the W = 8
(ii) Number of green marbles = 4
The number of outcomes favourable to the G = 4
Step 3: Calculate the probability
The probability to draw red marble P(R)= \frac{\text{ favourable outcomes}}{\text{Total possible outcomes}} = \frac{5}{17}
Similarly,
The probability to draw white marble P(W) = \frac{8}{17}
The probability to draw green marble P(G) = \frac{4}{17}
Note that P(W) + P(G) + P(R) = 1.