Some examples
Equally likely outcomes
If the experiment is of such a nature that we can assume equal weights for the sample points of S, i.e “Have same probability to occur”
Ex:- the roll of a fair die, in which the sample space is {1,2,3,4,5,6} and each of these outcomes has probability 1/6
Then the probability of any event A is the ratio of the number of elements in A to the number of elements in S.
P(A)=n(A)/n(S)
Example:
Find the probability of not getting a 3 or 5 while throwing a die.
Sol:
s={1,….,6} and event B={1,2,4,6}then p(B)=n(B)/n(s)=4/6=0.6667.
Note: A and B are complementary events. i.e B=?
so p(B)=P(?)=1-p(?)
For example,
A={3,5}, B={1,2,4,6}
p(B)=P(?)=1-p(?)=1-0.333=0.6667
Example
The experience of pulling a number from a box contains the number 1,2,3,4,5,6 and note any number will appear.
A: appear number greater than 3 ={4,5,6}=n(A)=3
B: appear number a smaller than 6={1,2,3,4,5}=n(B)=5
C: appear of an even number {2,4,6}=n(C)=3
Descripts the ?={1,2,3} , B ?, C ?, ??B ?, (B?A) ?,
?={1,2,3} appear number less than 4,
B ?={6} appear number greater than 5,
C ?={ 1,3,5 }
??B ?={ } appear number less than 4 and greater than 5,
(B?A) ? ={ } not greater than 3 or smaller than 6