Example 2: Board of Studies Syllabus, p33.

In a raffle, 30 tickets are sold and there are 2 prizes. What is the probability that someone buying 5 tickets wins at least 1 prize?

ANSWER

First, recognize that there 2 draws and that the sample space will be 1 less in the second draw. If one of the 5 tickets wins in the first draw, the event occurs and the outcome of the second draw is irrelevant. If the first draw is not successful, the probability of the event depends on the second draw.

From first principles,

$$\begin{array}{lcll} P(W) & = & P(W_1) & + P(W_2\vert L_1... ...{{25} \over {29}} \right) & = {{9} \over {29}} \\ \end{array}$$

The tree algorithm for deriving the above is plotted in Figure 6.

Figure 6: Probability Tree Example 2