7.1 Probability of an Event - SPM Additional Mathematics

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

P (A) = \frac{number of outcomes of event A}{number of outcomes of sample space S}

P (A) = \frac{n (A)}{n (S)}

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 complement of an event A is denoted by ̅A and the probability of a complementary event is given by

P (\bar{A}) = 1 - P (A)

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 (A) = \frac{n (A)}{n (S)} \\ = \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

\begin{array}{l} P (B) = \frac{n (B)}{n (S)} \\ = \frac{5}{20} = \frac{1}{4} \end{array}