# Independent Probability

Independent probability – one event **DOES NOT** affect the outcome of the other.

This woman is not dependent on anyone else to survive, she will **never** catch **i****nfluenza** (influence).

Independent probability - NOT Influenced

**Example 1**

A bag contains 6 marbles, four red and two yellow. A marble is taken from the bag, its colour written down then it is returned to the bag. A marble is again taken from the bag, and its colour written down.

1. What is the probability of getting two red marbles?

2. And what is the probability of getting a red and a yellow marble?

Start by drawing a probability tree:

This can be redrawn as:

This is the probability tree for this example.

Add these up to check they equal 1 `16/36+8/36+8/36+4/36=(16+8+8+4)/36=36/36=1`

I. Therefore from the diagram above the probability of getting two red marbles is:

Red, Red =`16/36=8/18=4/9`

Probability of two reds is 4 in 9 or = 0.44 And if 1 = 100% then 0.44 = 44% chance.

II. What is the probability of getting a red and a yellow marble?

Add

`8/36+8/36=(8+8)/36=16/36=8/18=4/9`

The probability of getting a red and a yellow marble is 4 in 9 or = 0.44.

And if 1 = 100% then 0.44 = 44% chance.