**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:**

## 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.

**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.

**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

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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

**Step 2****:**

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

**Step 3:**

At the end of each branch, write one of the three options from the 2^{nd} 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:**