# Probability

Consider the following

(i) Student who has maximum weight in your class

(ii) Marks scored by you in the final exam in mathematics

(iii) Selecting a red color ball from a bag of balls

(iv) Ice cream favored by maximum number of students in your class.

Study the above four situations. You can find the student who has maximum weight in your class and ice cream favoured by maximum number of students in your class.

Can you find the mark which will you get in your final exam?

You may get more than 90, 65, or 80.

Can you select a red color ball from a bag of balls?

The ball may be red, white, or some other colour.

In these kinds of situations we cannot predict the answer. Let us see what probability is and terms involved in probability.

Experiment
The following situations are known as experiment.

Experiment

An experiment is a situation involving chance or probability that leads to results.

Random Experiment

A Random Experiment is an experiment, trial, or observation that can be repeated numerous times under the same coonnditis. Outcome of random experiment cannot be predicted with certainity. Tossing a coin and rolling a die are some examples of Random experiment.

Outcome

An outcome is the result of a single trial of an experiment.

 Experiment Rolling a die Outcome   1, 2, 3, 4, 5 or 6 tossing a coin Head or Tail

Event

An event is one or more outcomes of an experiment.

 Experiment Rolling a die Event (i) Getting the number 5 (ii) Getting the number 6 tossing a coin (i) Getting head (ii) Getting tail

Probability

The probability of event A is the number of ways event A can occur divided by the total number of possible outcomes.

It is a way of summarizing the uncertainty of statements or events.

 Experiment Rolling a die Probability Getting the number 5 tossing a coin Getting Head

Example

A single 6-sided die is rolled. What is the probability of rolling an even number or rolling an odd number?

Solution

The outcomes are {1, 2, 3, 4, 5, 6}

Total number of outcomes = 6.

Probability of getting an even number

Probability of getting an odd number

Equally likely Outcomes
Two or more possible outcomes of a given situation that have the same probability.

Example : Picking a card from a pack of cards. If you and your friends are going to pick a card means, every card has equal chance of being picked.

In a rolling a die, both the events getting head and tail are equally likely outcomes.