# Probability

__Introduction__

Probability is the **likelihood** or **chance** of an event occurring.

Probability = the number of ways of achieving **success** / the **total** number of possible outcomes

For example, the **probability** of **flipping** a coin and it **being heads** is **½,** because there is **1** way of **getting a head** and the **total number** of possible outcomes is **2** (a head or tail). We write P(heads) = ½ .

The probability of something which is

**certain**to happen is**1**.The probability of something which is

**impossible**to happen is**0**.The probability of something

**not happening**is**1 minus**the**probability**that it will**happen**.

__Single Events__

**Example:**

There are **6** beads in a bag, 3 are red, 2 are yellow and 1 is blue. What is the probability of picking a **yellow**?

The probability is the **number of yellows** in the bag **divided** by the **total** number of balls, i.e. 2/6 = 1/3.

**Example:**

There is a bag full of coloured balls, red, blue, green and orange. Balls are picked out and **replaced**. John did this **1000 times** and obtained the following results:

Number of blue balls picked out: 300

Number of red balls: 200

Number of green balls: 450

Number of orange balls: 50

a) What is the probability of **picking** a **green** ball?

*For every 1000 balls picked out, 450 are green. Therefore P(green) = 450/1000 = 0.45*

b) If there are **100 balls** in the bag, how many of them are **likely** to be **green**?

*The experiment suggests that 450 out of 1000 balls are green. Therefore, out of 100 balls, 45 are green (using ratios).*

__Multiple Events__

__Independent and Dependent Events__

Suppose now we consider the **probability of 2 events happening**. For example, we might **throw 2 dice** and consider the probability that **both are 6's**.

We call two events **independent** if the **outcome of one** of the events **doesn't affect** the **outcome of another**. For example, if we throw two dice, the **probability of getting a 6** **on the second **die is the same, **no matter** **what we get** **with the first** one. It's still 1/6.