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 eventAnumber of outcomes of sample spaceS
P(A)=n(A)n(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(ˉA)=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
P(A)=n(A)n(S)=1020=12
(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)=520=14