How to estimate Probability with example

Introduction:

      Probability is an estimate of the likelihood of the occurrence of an event. An event is a set of possible outcomes resulting from a particular experiment. For example, estimate a possible event when a single six - sided numbered cube is rolled is {1, 4}. That is, the roll could be a 1 or a 4. In general, an event is any subset of a sample space (including the possibility of an empty set).

Estimate Probability – Examples

Example 1: Estimate the probability that an actor will get a film is ‘3/5’ and the probability that he will get on other film is 6/11. If the probability of getting at least one film is 5/7, what is the probability that he will get both the films?

Solution:

Here P(A) = 3/5, P(B) = 6/11

P(A or B)  =  5/7,  (P(A and B) = ?

By addition rule of probability:

P(A or B)  =  P(A) + P(B)  - P(A and B)

= 5/7  =  3/5 + 6/11  -  P(A and B)

or 5/7  =  63/55 – P(A and B)

or P(A and B)  =  63/55 – 5/7 = 166/385

P(A and B) =  166/385

Hope you like the above example. Please leave your comments, if you have any doubts.