Advanced Probability and Statistics

 In math, advanced probability is a way of expressing knowledge or belief that an event will occur or has occurred.Advanced probability is used to find the positive outcomes.Statistics is the official science of making successful use of numerical data relating to groups of individuals or experiments. Now we will see the examples for advanced probability notes and statistics notes. 


Example for Advanced Probability


     In a bowl there are 40 balloons available. In that balloons there are 10 red balloons, 10 blue balloons and 20 green balloons available. Find the probability of the following conditions.

i) Select the red balloons.

ii) Select the green balloons.


     Total balloons n(S) = 40

     Red balloons n (A) = 10

     Blue balloons n (B) = 10

     Green balloons n(C) =20

     i) Assume the P(A) is the probability for choose Red balloons .

            P(A)= n(A)/n(S)

                   = 10/40

                   = 1/4

     ii) Assume the P(C) is the probability for choose green balloons.

            P(C) =n(C)/n(S)

                    =20 / 40



Example for Statistics


What is the mean, median,mode,range of the following number series in statistics.



     The given numbers are 3,4,6,7,9,12,14.


     Usually mean is the average of the given number. So first find the addition of the given numbers and divided by the total number.

     Addition of the given numbers are = 3+4+6+7+9+12+14

                                                       = 55.

     Now divided by 7(Notes: 7 is the total given numbers total) = 55 / 7

                                                                                          = 7.85


     It is a center value of the given series.

     The center value of the above series is 7.

     So 7 is the median of the given series.



     Mode is a frequent value of the given number series. There is no frequent value in this series.

    So the mode is null.


     The difference between highest value and the lowest value is known as the range of the series.


     So 11 is the range of the series.