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Classical Probability

The probability of any event is an expression of likelihood of occurrence of an event. The classical approach to probability is the simple. In classical theory, the outcomes of a random experiment are equally likely. The classical probability is defined as the ratio of the number of favorable outcome of the event to the total number of events. The each of the outcomes must be equally likely. Function is gained from real occurrences in long-run occurrence and experimentation. 

Formula for classical probability:

P (A) = ` ("Total number of outcomes favorable to A")/("Total number of possible outcome")"

                     
Examples of Classical Probability:

Example 1:

Suppose that twenty files were presented to Jhon for removal. Five files contained wrong entry. All the files were in detail mixed in there was no indication about files with wrong entries. What is the probability that 1 file with false entry is chosen.

Solution:
Total number of files, n(S) = 20

Let A be the event the file has wrong entry.

Number of files contained wrong entry, n(A) = 5

By classical definition of probability. All the 20 files are assumed to be same likely for the purpose of selecting a file.

Now, probability of selecting a file with wrong entry is writing as P(A), so

P(A) =  `("Number of outcomes favorable to A")/("Number of possible outcomes")"="(n(A))/(n(S))`

= 5/20

= 1/4

Example 2:

A die is thrown. To calculate probability that the face on the die is greatest, major, compound of 3.

Solution:

There are 6 possible outcomes when a die is thrown. We calculate that all the 6 faces are equally possible outcomes.

The sample space is S = {1, 2, 3, 4, 5, 6} => n(S) = 6

Let A be the event the face is greatest

Thus, A = {6} => n (A) = 1

P(A) = `(n(A))/(n(S))` = 1/6

Let B be the event that the face is greatest

B = {2, 3, 5} => n (B) = 3

P (B) =`(n(B))/(n(S))` = 3/6 =1/2

Let C be the event that the face is greatest.

C = {3, 6} => n(C) = 2

P(C) = `(n(C))/(n(S))` = 2/6 = 1/3

          

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