explain the concept of probability with examples.
Answers
Step-by-step explanation:
Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The simplest example is a coin flip. When you flip a coin there are only two possible outcomes, the result is either heads or tails
We often hear statements like "It is likely to rain today.". "Most probably India will beat Pakistan in the cricket World Cup.". "It is impossible to find a 1-m-long ant.", etc. In all of these statements, people are predicting the likelihood of something happening or not happening.
Probability is the study of the likelihood of an event happening under a given set of conditions.
There are two possible outcomes in the toss of a coin. So, the chance of getting heads is fifty-fifty.
Then, we say that the probability of getting heads is 1/2. Similarly, the probability of getting tails is 1/2.
If a bag contains three balls-one each of the red, green and blue colours. and a ball is chosen at random, the possible outcomes are three-one red ball. one green ball and one blue ball. So, the chance, or the possibility, of getting a red ball (or a green ball or a blue ball) is one third, i.e. 1/3
Therefore, probability of getting a red ball = 1/3
Probability of an event
Probability of an event= No. of favourable outcomes for the event/ Total no. of possible outcomes in an experiment.
Probability scale
Probabilities are measured on a scale from 0 to 1. A probability of 0 means that there is no chance of an event happening. A probability of 1 means that the event will happen certainly.
The probability of an event happening is never negative.
Sure event
An event which is certain to happen is called a sure event. The probability of a sure event is 1.
Examples (1) In the throw of a die, the event of getting a positive integer less than 7 is a sure event. So, its probability is 1.
(2) When a ball is chosen at random from a bag of white balls only. the event of getting a ball of the white colour is a sure one. So, its probability is 1.
Impossible event
An event which is impossible to happen is called an impossible event. The probability of an impossible event is 0.
Examples (1) The event of getting a natural number greater than 6 in the throwof a die is an impossible event. So, its probability is 0.
(2) The event of picking a ball of the white colour from a bag of green and red balls only is an impossible one. So, its probability is 0.
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Solved example
A five-rupee coin is tossed. Find the probabilities of getting (i) heads (ii) tails.
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In the toss of a coin, the possible outcomes are heads and tails.
So, the total number of outcomes is 2.
(1) Number of heads = 1.
So, the number of favourable outcomes is 1.
Therefore, the probability of getting heads is
P(getting heads) = no. of heads/total no. of outcomes
= 1/2.
(ii) Number of tails = 1.
So, the number of favourable outcomes is 1.
Therefore, the probability of getting tails is
P(getting tails) = no.of tails/total no. of outcomes
= 1/2.
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Hope you have understood.