Probability Formula by tutorvistateam123


									                          Probability Formula
Probability Formula

Probability as the name suggests deals with uncertainty. In mathematics this is calculated and
the process is called as probability.

It is one of the most important concepts of mathematics. Solving probability problems is not
easy but with good probability help from expert tutorvista tutors makes it easy and simple to
deal with. It includes concepts and formulas and how to solve problems using the formula.

These all concepts are explained to you by our tutors with step by step explanation. Get your
probability help from expert tutors now!

Free Probability Help Online

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Multiplication Rule of Probability

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We have already proved that if two events A and B from a sample S of a random experiment
are mutually exclusive, then

In this section, we examine whether such a rule exists, if '' is replaced by '' and '+' is replaced
by 'x' in the above addition rule. If it does exist, what are the particular conditions restricted on
the events A and B.

This leads us to understand the dependency and independence of the events.

Example :

A bag contains 5 white and 8 black balls, 2 balls are drawn at random. Find

a) The probability of getting both the balls white, when the first ball drawn, is replaced.
b) The probability of getting both the balls white, when the first ball is not replaced.


a) The probability of drawing a white ball in the first draw is . Since the ball is replaced, the
probability of getting white ball in the second draw is also .

b) The probability of drawing a white ball in the first draw is . If the first ball drawn is white and
if it is not replaced in the bag, then there are 4 white balls and 8 black balls. Therefore, the
probability of drawing a white ball in the second draw = .

In this case, the probability of drawing a white ball in the 2nd draw depends on the occurrence
and non-occurrence of the event in the first draw.

he probability simulations learning utilize the concepts of theoretical and experimental
probabilities to solve problems involving uncertainty.

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The probability simulations learning to perform the model of real-world situations involving
uncertainty. We can conduct probability simulations of the results for many problems of
objects we pick should have the same number of results as the number of possible results of
the problem, and all outcomes should be equally likely.

Theoretical and Experimental Probability

Theoretical probabilities of operations are performed in mathematically and describe what
should happen.

Experimental probability is calculated using data from tests or experiments. Experimental
probability is the ratio of the number of times an outcome happened to the total number of
events or trials. This type of ratio is labeled as the relative frequency.

Experimental probability = (Frequency of an outcome)(Total number of trials)

Empirical study or learning:

It is helpful to perform an experiment repeatedly, collect and combine the data, and analyze
the results. This is known as an empirical study or learning.                                                  Page No. :- 4/4
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