**7.1 Probability of an Event**

**1.**An

**is a process or an action in making an observation to obtain the require results.**

*experiment***2.**An

**of an experiment is a possible result that can be obtained from the experiment.**

*outcome***3.**A

**of an experiment is the set of**

*sample space***of an experiment.**

*all the possible outcomes***4.**The probability for the occurrence of an event A in the sample space

*S*is

$\overline{)\text{}P(A)\text{=}\frac{\text{numberofoutcomesofevent}A}{\text{numberofoutcomesofsamplespace}S}\text{}}$

$\overline{)\text{}P(A)\text{}=\text{}\frac{n(A)}{n(S)}\text{}}$

$\overline{)\text{}P(A)\text{}=\text{}\frac{n(A)}{n(S)}\text{}}$

**5.**

**(a)**The range of values of a probability is .

**(b)**If

*P*(

*A*) = 1, event

*A*is

**.**

*sure to occur***(c)**If

*P*(

*A*) = 0, event

*A*

**.**

*will not occur***6.**The

**of an event**

*complement**A*is denoted by ̅

*A*and the probability of a complementary event is given by

$\overline{)\text{}P(\overline{A})=1-P(A)\text{}}$

**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}

*n*(

*S*) = 20

**(a)**

*A*= Event of obtaining an even number

*A*= {22, 24, 26, 28, 30, 32, 34, 36, 38, 40}

*n*(

*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}

*n*(

*B*) = 5