Solving Probability

SOLVING PROBABILITY

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

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Total number of possible outcomes

Example (1) :

A fair coin is tossed three times. Find the probability of getting at least . two heads.

Solution :

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

Is ½.

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

committee.

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.