Topic Content:
- Tree Diagrams
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
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