Do you ever leave anything to ‘chance’? Like perhaps leave out a chapter from your revision because it ‘probably’ won’t come in an exam? These terms ‘chance’ and ‘probability‘ can actually be expressed in mathematical terms. Come let us take a closer look at probability and the probability formula.

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## Chance and Probability

Let us explain both these concepts with an example. You have gathered your friends to come and play a friendly board game. It is your turn to roll the dice. You really need a six to win the whole game. Is there any way to guarantee that you will roll a six? Of course, there isn’t. What are the chances you will roll a six?

Well if you apply the basic logic you will realize you have a one in six chance of rolling a six. Now based on the above example let us look at some concepts of probability.

#### Probability

Probability can simply be said to be the chance of something happening, or not happening. So the chance of an occurrence of a somewhat likely event is what we call probability. In the example given above the chance of rolling a six was one is six. That was its probability.

#### Random Experiment

A process which results in some well-defined outcome is known as an experiment. Here you rolling the dice was the random experiment, since the outcome was not sure. The outcome here is 1, 2, 3, 4, 5, or 6. It cannot be predicted in advance, making the rolling of dice a random experiment.

#### Sample Space

All possible outcomes or results of an experiment make up its sample space. So the sample space of the above example will be, S = { 1,,2,3,4,5,6}. Since a dice once thrown can give you only one of these six results.

#### Event

When a particular event occurs, like for example the dice lands on a six, we can say an event has occurred. So we can say every possible outcome of a random experiment is an event.

#### Equally likely Events

Let us now change our example. Say you are now tossing an ordinary coin. Every time you toss it either land on heads or on tails. Every time the coin gets tossed there is a 50% chance of heads and 50% chance of tails. Both events are equally likely, i.e. they have an equal chance of happening. This is what we call Equally likely events.

#### Occurrence of an Event

A particular event will be said to occur if this event E is a part of the Sample space S, and such an event E actually happens. So in the above experiment, if you actually roll a six, the event will have occurred.

## Probability Formula

Now that we have seen the concepts related to probability, let us see how it is actually calculated. To see what are the chances that an event will occur is what probability is. Now it is important to remember that we can only calculate mathematical probability of a random experiment. The equation of probability is as follows:

P (E) = Number of desirable events ÷ Total number of outcomes

Using this formula let us calculate the probability of the above example. Here the desirable event is that your dice lands on a six, so there is only one desirable event. And the total number of possible results, i.e. the sample space, is six. So we can calculate the probability, using the probability formula as,

P (E) = 1/6

## Solved Example for You

**Question 1: Toss a fair coin 3 times in a row, how many elements are in the sample space?**

**2****4****6****8**

**Answer :** The correct answer is “D”. The Sample Space of a collection are all the possible events. Here there are 8 possible events that can occur. Hence S = {H,H,H} {H,H,T} {H,T,T} {H,T,H} {T.T.T} {T,T,H} {T,H,H} {T,H,T} = 8

**Question 2: A die is thrown once. The probability of getting a number greater than 3 is ___?**

**1 / 2****1/3****1****2/3**

**Answer :**The correct answer is “A”. Numbers on a dice greater than three are 4, 5 and 6. Using probability formula we get P(E) = 3/6 = 1/2

**Question 3: What meant by simple probability?**

**Answer: **Simple probability refers to the ratio of the number of outcomes that are favourable for the particular event to the total number of possible outcomes. So, probability refers to a measure of the likelihood of an event.

**Question 4: Explain probability with example?**

**Answer:** One can understand probability with the example of a flipping coin. The probability of getting head after flipping a coin is ½. This is because there is one way of getting a head while the total number of possible outcomes happens to be 2. The probability will be 1 for anything that is certain to happen. The probability will be 0 for something that is impossible to happen.

**Question 5: What is the purpose or importance of probability?**

**Answer:** Purpose of probability is finding out the percentage of the possibility of occurrence of an event. Probability allows us to make a prediction of happening. It allows us to get a rough idea regarding the happening of an outcome.

**Question 6: How can one calculate simple probability?**

**Answer:** One can calculate simple probability by doing division of the number of events with the number of possible outcomes.

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