Topic 6: Probability

Define:
Probability is the chance that something will happen - how likely it is that some event will happen.

For a sample space S with a finite number of equally likely outcomes.

Probability of an event E,


Where n (E) is the number of possible outcomes in the event E, n (S) is the number of possible outcomes in the sample space S.



Example 1,

There are 10 balls in a bag. One is Red, two are Blue, three are Yellow and four are Green. A ball is taken out without looking. What is the probability that it is.

Example 2,

The probability that a football team will win their next match is 1/4. What is the probability that the team will not win?




Tree Diagram

Independent events and their probabilities can be shown on a tree diagram. Each event is represented by a branch.

Example 1,

A coin is flipped twice. Draw a thee diagram to show all the possible outcomes.

Outcomes Probabilities
 HH 1/2 x 1/2 = 1/4






HT 1/2 x 1/2 = 1/4
TH 1/2 x 1/2 = 1/4






TT 1/2 x 1/2 = 1/4