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
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