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Probability and trees

Introduction to Probability and Trees:

In mathematics, the probability tree mechanism is used to simplify the most probability problems .It is gives a methodical function of generating the elements of an appropriate section space and determining their probabilities. Here we will see the examples for the probability tree.


Creation of Probability Tree

Probability trees growing from left to right. Sometimes it will growth from top to bottom. The root of the tree communicates to the initial point of the process. Here branches are the line segments. It is connected the root to nodes denoting the various outcome.

Example:

In a box, there are 4 red pens, 3 black pens and 2 green pens. One pen is chosen randomly from the box. If red or green pen is selected, a faircoin is tossed one time. It the pen is black, the coin is tossed twice.We can create a tree to these outcomes.

Step 1:

     A pen is selected and its color is noted.Red, Black, Green denoted by R, B,G.

      Firststepoftreecreation.

Step 2:

     The coin is tossed. Head and tail denoted by H and T.Now we get the following tree structure.

     Thistreecreatedaftertossedthecoin.

The above two steps are used to creating the probability tree.

Between, if you have problem on these topics Probability Distribution Example , please browse expert math related websites for more help on Central Limit Theorem Example .

Example for Probability

In a school there are 150 students are available. In those students 50 students wear green colour dress. 60 students wear red colour dress and remaining 40 students wear yellow colour dress. Find probability and trees of the students entering in class in the following way.

  a)The students leaving who one wear the green colour dress.

  b)The student leaving who one wear red colour dress.

Solution:

a) Let S is the sample space and A is the event of the students leaving who wear the green colour dress .

n(S)=150

n(A)=50

So the probability is P(A) =50/150

= 1/3

 b) Let S is the sample space and B is the event of the students leaving who wear the red colour dress .

         n(S)=150

         n(A)=60

         So the probability is P (A) =60/150

                                               = 6/15

     We can draw the probability tree to this method.