Classical Definition of PROBABILITY
If an experiment can result in a certain number of possible outcomes N, then the probability of the occurrence of an event A is:
number of occurrences of A
Total number of possible outcomes
Example (1) :
A fair coin is tossed three times. Find the probability of getting at least . two heads.
Let A = be the event of getting at least two heads
Let S = Sample Space which refers to the total number of possible outcomes
S = ( HHH, HHT, HTH, THH, HTT,THT,TTH,TTT ) = 8
A = ( HHT, HTH, THH, HHH ) = 4
P(A) = 4/8 = 1/2
The probability of getting at least two heads when a coin is tossed three times
Example ( 2 ) :
To form a committee, four people are to be selected from a group of five
doctors and five lawyers. Find the probability of including two doctors in the
First find the Sample Space which is total number of possible committees
consisting of four members selected from ten members.
Sample Space = 10 C 4 = 10 !/ (10 - 4)! 4! = 210
Next find the number of possible committees formed consisting of two doctors.
Let this be n.
n = 5 C 2 * 5 C 2 = 5! / 3! 2! * 5!/3! 2!
= 10 * 10 = 100
P(A) = n / Sample Space = 100 / 210 = 10/ 21
The probability of including two doctors in the committee is 10/21.