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 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( A ¯ )=1P(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
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}
n(B) = 5
P( B )= n( B ) n( S )         = 5 20 = 1 4