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

P ( A ) = number of outcomes of event A number of outcomes of sample space S  
P ( A ) = n ( A ) n ( S )

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
P ( 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}
(S) = 20

(a)
A = Event of obtaining an even number
A = {22, 24, 26, 28, 30, 32, 34, 36, 38, 40}
(A) = 10
P ( A ) = n ( A ) n ( S ) = 10 20 = 1 2

(b)
B = Event of obtaining an odd number greater than 29
B = {31, 33, 35, 37, 39}
(B) = 5
P ( B ) = n ( B ) n ( S ) = 5 20 = 1 4


Leave a Comment