Have you found yourself in a situation where you need to predict which is right in a situation or an outcome of a particular event? That’s probability.

Probability is a a branch of mathematics that deals with the occurrence of a random event in a given trials. Or the likelihood or chance of an event occurring.

The probability of throwing 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 Pr(heads) = ½.

## Terms used in probability

Event : An event is any possible set of outcomes. In rolling a die, an event E is defined as “E: 3 is not obtained”. which leaves the outcome to be (1,2,4,5,6).

Outcome: An outcome is any one of the possible results of the experiment. obtaining a 4 when a die is rolled is an example of an outcome in an experiment.

Sample space : The sample space is the set of all possible outcomes in a random experiment.

Equally likely outcomes: Equally likely outcomes of an experiment are outcomes with the same chance of occurrence. That is, upon performing the experiment a large number of times, the relative occurrences of the two outcomes turn out to be equal.

Random experiment : In a Random experiment, the possible outcomes are known but cannot be said prior to performing the experiment. e.g rolling a die e.t.c

Probability: The probability of an event occurring or not is given as a ratio of the favorable outcome and number of possible outcomes.

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## Types of Event

There are two types of Event; Dependent and Independent event.

1. Dependent Event: In a dependent event, the probability of one event depends on another. example ; in a bag containing 2 red and 2 blue balls. If we pick 2 balls out of the bag, the probability that the second is blue depends upon what the colour of the first ball picked was.

2. Independent Event: For an independent Event, the outcome of one of the events doesn’t affect the outcome of the other. e.g rolling two dice, the probability of getting a 1 on a die is always ⅙, no matter what was gotten in the other. They are not dependent of each other.

## What to note in probability

• If the outcome of an event is certain, the probability is 1

• When the outcome is impossible, the probability is 0

• The probability of an event occurring is 1 minus the probability of it not occurring.

## How to determine a probability.

• Get a single event with a single outcome.
• Identify the total number of possible outcomes
• Divide the number of events by the number of possible outcomes.
• Determine each event you will calculate.
• Calculate the probability of each event.

## 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?

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

A careful application of the above explanation will make it easy to solve any probability question, with more emphasis on Careful Application.
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