__Probability__

**Probability**is the measure of the likeliness that an event will occur.

**Probability**is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the

**probability**of an event, the more certain we are that the event will occur. A simple example is the toss of a fair (unbiased) coin. Since the two outcomes are equally probable, the probability of "heads" equals the probability of "tails", so the probability is 1/2 (or 50%) chance of either "heads" or "tails".

Day 1

One way to find the probability of an event is to conduct an experiment.

A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the experimental probability of getting a blue marble.

Take a marble from the bag.

Record the color and return the marble.

Repeat a few times (maybe 10 times).

Count the number of times a blue marble was picked (Suppose it is 6).

The experimental probability of getting a blue marble from the bag is 6/10 = 3/5.

__Theoretical and Experimental Probabilities__

__Experimental Probability__One way to find the probability of an event is to conduct an experiment.

*Example:*A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the experimental probability of getting a blue marble.

*Solution:*Take a marble from the bag.

Record the color and return the marble.

Repeat a few times (maybe 10 times).

Count the number of times a blue marble was picked (Suppose it is 6).

The experimental probability of getting a blue marble from the bag is 6/10 = 3/5.

**Theoretical Probability**We can also find the theoretical probability of an event.

The formula for theoretical probability of an event is:

P(event) = Number of favourable outcomes ÷ Number of total outcomes

**__Example 1__:A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the theoretical probability of getting a blue marble.

__Solution:__There are 8 blue marbles. Therefore, the number of favorable outcomes = 8.

There are a total of 20 marbles. Therefore, the number of total outcomes = 20

P(event) = Number of favourable outcomes ÷ Number of total outcomes = 8/20 = 2/5

**__Example 2:__Find the probability of rolling an even number when you roll a die containing the numbers 1-6. Express the probability as a fraction, decimal, ratio and percent.

*Solution:*The possible even numbers are 2, 4, 6. Number of favorable outcomes = 3.

Total number of outcomes = 6

P(event) = Number of favourable outcomes ÷ Number of total outcomes = 3/6 = 1/2

The probability = 1/2 (fraction) = 0.5 (decimal) = 1:2 (ratio) = 50% (percent)

**Day 2**

__Calculating Probability__