Probability Fractions

Probability is a method of expressing knowledge or belief that an event will occur or has occurred. In mathematics the theory has been given an exact meaning in probability theory, which is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions. Now we are about to see the probability fractions.

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Sample probability fractions problem:

             When two coins are tossed at the same time, then what is the probability of getting (i) only one head (ii) two heads (iii) almost one head. Determine the probability fractions.

Solution:

            Now we are going to find the probability given as follows,

            The sample space is S = {HH, HT, TH, TT}, n(S) = 4

             Let us assume X be the event of getting only one head, Y be the event of getting two heads and Z be the event of getting atmost one head.

                  P = {HT, TH}, n(X) = 2

                  Q = {HH}, n(Y) = 1

                  R = {HT, TH, HH}, n (Z) = 3

         (i) P (X) = (n(X)/ n(S)) = `2/4` = `1/2`

         (ii) P (Y) = n (Y) /n(S) = `1/4`

         (iii) P (Z) = n (Z)/n(S) = `3/4`

More problems for probability fractions:

           Now we are going to see about the probability fractions examples.

Example 1:

        Determine the range of the data 20, 25, 30, 35, 40, 50 and also determine the coefficient of range.

Solution:

          Now we are going to calculate the probability range.

          Largest value L = 50; Smallest value S = 20

          Range = L - S = 50 - 20 = 30

          Range  Coefficient = `(L - S) / (L + S)`

                                      = `(50 - 20) / (50 + 20)`

                                      = `30/70`

                                      = `3/7`

Algebra is widely used in day to day activities watch out for my forthcoming posts on Simplify a Rational Expression and Measurement of Central Tendency. I am sure they will be helpful.

Example 2:

              At a parking area, there are about 150 vehicles, 60 of which are bicycles, 30 are bikes and the remaining are  tricycle. If every vehicle is equally, willing to leave, determine the probability of:

a) Bike leaving first.

b) tricycle leaving first.

Solution:

a) Let S be the sample space and E be the event of a van leaving first.

n (S) = 150

n (E) = 30

Probability of a bike leaving first:

P (E) = `30/150` = `1/5`

b) Let F be the event of a tricycle leaving first.

n (F) = 150 - 60 - 30 = 60

P(F) = `60/150 ` = `2/5`