Notes on Probability
Probability
Probability is the study of mathematics which calculates the degree of uncertainty. There are two types of approaches to study probability-
1. Experimental or Empirical Probability
The result of probability based on the actual experiment is called experimental probability. In this case, the results could be different if we do the same experiment again.
2. Probability — A Theoretical Approach
In the theoretical approach, we predict the results without performing the experiment actually. The other name of theoretical probability is classical probability.
Where the outcomes are equally likely.
Equally Likely Outcomes
If we have the same possibility of getting each outcome then it is called equally likely outcomes.
Example
A dice have the same possibility of getting 1, 2, 3, 4, 5 and 6.
Not Equally Likely
If we don't have the same possibility of getting each outcome then it is said to be the not equally likely outcome.
Example
3 green balls and 2 pink balls are not equally likely as the possibility of the green ball is 3 and the possibility of the pink ball is 2.
Elementary Event
If an event has only one possible outcome then it is called an elementary event.
Remark
The sum of the probabilities of all the elementary events of an experiment is 1.
The General form
P (Heads) + P (Tails) = 1
P (H) + P
= 1 where
is ‘not H’.
P (H) – 1 = P
P (H) and Pare the complementary events.
Impossible Events
If there is no possibility of an event to occur then its probability is zero. This is known as an impossible event.
Example
It is not possible to draw a green ball from a group of blue balls.
Sure or Certain Event
If the possibility of an event to occur is sure then it is said to be the sure probability. Here the probability is one.
This shows that the probability of an event could be
0 ≤ P (E) ≤ 1
Some Solved Examples
Example: 1
What is the probability of drawing a heart from a deck of cards?
Solution:
We know that there are total 52 cards in a deck out of which 13 cards are of heart.
So the favourable outcomes are 13 and the total no. of events is 52.
= 13/52 = 1/4
Example: 2
If we toss two coins together, then what is the probability of getting at least one tail?
Solution:
If we toss two coins together then the total outcomes could be
The favorable outcomes for at least one head will be
{HH}, {HT}, {TH} = 3
P (for at least one head) = 3/4
Important Tips
- Coin: A coin has two faces termed as Head and Tail.
- Dice: A dice is a small cube which has between one to six spots or numbers on its sides, which is used in games.
- Cards: A pack of playing cards consists of four suits called Hearts, Spades, Diamonds and Clubs. Each suite consists of 13 cards.
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