7.1 Probability of an Event

7.1 Probability of an Event

1. An experiment is a process or an action in making an observation to obtain the require results.
2. An outcome of an experiment is a possible result that can be obtained from the experiment.
3. A sample space of an experiment is the set of all the possible outcomes of an experiment.
4. The probability for the occurrence of an event A in the sample space S is

$\overline{)\text{}P\left(A\right)\text{=}\frac{\text{number of outcomes of event}A}{\text{number of outcomes of sample space}S}\text{}}$
$\overline{)\text{}P\left(A\right)\text{}=\text{}\frac{n\left(A\right)}{n\left(S\right)}\text{}}$

5.
(a) The range of values of a probability is .
(b) If (A) = 1, event is sure to occur.
(c) If (A) = 0, event A will not occur.

6. The complement of an event A is denoted by ̅A and the probability of a complementary event is given by
$\overline{)\text{}P\left(\overline{A}\right)=1-P\left(A\right)\text{}}$

Example:
A box contains 20 cards. The cards are 21 to 40 respectively. If a card is chosen at random, find the probability of obtaining
(a) an even number,
(b) an odd number greater than 29.

Solution:
The sample space, S, is
S = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}
(S) = 20

(a)
A = Event of obtaining an even number
A = {22, 24, 26, 28, 30, 32, 34, 36, 38, 40}
(A) = 10
$\begin{array}{l}P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}\\ \text{}=\frac{10}{20}=\frac{1}{2}\end{array}$

(b)
B = Event of obtaining an odd number greater than 29
B = {31, 33, 35, 37, 39}
(B) = 5
$\begin{array}{l}P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}\\ \text{}=\frac{5}{20}=\frac{1}{4}\end{array}$