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Probability tree

Introduction to Probability:

Theprobability is number of outcomes is divided into total number of events this is called the probability. These are the two types of distribution are used discrete and continuous distribution.  The generalformat of the probability

The probability of Event P (A) = ` "No. of outcomes n(a)"/"Total no. of events n(s)" `

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Tree Diagram

A schematic device useful in determining the sample space for an experiment or design and in computing probabilities

Example of probability tree:

 ExampleforProbabilityTree


Probability Tree - Examples


Probability Tree - Example 1:

Use tree diagrams to find probabilities

A bag contains 3 blue and 5 red beads. When a bead is taken from the bag, it is replaced. Draw a tree diagrams to show all the probabilities for each case.


Example1ProbabilityTree

Probability Tree  - Example 2:

      A bag contains 2 blue and 4 red beads. When a bead is taken from the bag, it is not replaced. Draw a tree diagram to show all the possibilities of two beads being taken consecutively. Use tree diagrams to find probabilities

       Notice how the fractions alter when there is not replacement.

Example2ProbabilityTree

Probability Tree Diagram example 3:

Use tree diagrams to find probabilities. The probability that Alan willscore with a shot at goal, is 0.4. Alan has two shots at goal.

(a) Put all the probabilities onto the tree diagram.

(b) Calculate the probability that Alan will score

     (i) Two goals (ii) exactly one goal and  iii) no goals

Example3ProbabilityTree

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Probability Tree Diagram example 4:

How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue

Solution;

Step 1:

 Now find out how many choices there are for the second item

 There are 3 options:

Red

White

Blue

Example4ProbabilityTree

Step 2:

Draw “branches” off of each number. One for each second item, in this case 3


Example4ProbabilityTree2

Step 3:

At the end of each branch, write one of the three options from the 2nd items given. There are a total of 15 total choices listed

Step 4:

What is the chance of choosing the color red?

There are 5 special times the color red could be chosen from all 15 options

The chance of having the color red is `5/15` or reduced is` 1/3`


Practice Problems for probability tree:

Givethe total number of events of choosing a hamburger, hot dog, or chickenand potato salad, coleslaw, or beans. Use a tree diagram.

Answer: