Tree Diagrams

Topic Content:

A tree diagram is a systematic method used to display all possible outcomes of two or more successive events. Each branch of the tree diagram represents possible outcomes at a given stage.

Example 7.3.1:

The probability that one fails his physics test is \(\frac{3}{8}\). The probability that he fails his history. test is \(\frac{1}{4}\). Using a tree diagram, find the possibility that he:

(a) passes both subjects
(b) passes physics and fails history

Solution

• P = Pass
• F = Fail

(a) Pr (PP) = \( \frac{5}{8} \: \times \: \frac{3}{4} \\ = \frac{15}{32} \)

(b) Pr (PF) = \( \frac{5}{8} \: \times \: \frac{1}{4} \\ = \frac{5}{32} \)

Example 7.3.2:

A box contains 10 marbles, 7 of which are black and 3 are red. Two marbles are drawn one after the other without replacement. Find the probability of getting:

(a) a red then a black marble
(b) two black marbles