# Probability And Statistics

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```					                Probability And Statistics
When we are solving Conditional Probability Examples ,we deal with two events, say A
and B , sometimes these events are so related to each other , that the probability will
depend on whether the other event has already occurred.

Conditional probability can be defined as the probability of an event given that another
event has already occurred.

Let’s consider an example for Conditional probability: Consider a card game, suppose a
player needs to draw 2 cards of the same suit to win, out of 52 cards there can be 13
cards in each suit.

If the first player draws a heart, and the player wishes to draw a second heart. If one
heart has already been chosen, then we only have 12 hearts remaining out of 51 cards.

So the conditional probability P = 12/51

Know More About Formula for Slope
Let us consider the random experiment of throwing a die. Let A be the event of getting
an odd number on the die.

Let B = {2, 3, 4, 5, 6}. If, after the die is thrown, we are given the information, that the
event B has occurred, then the probability of event A will no more be 1/2, because in
this case, the favourable cases are two and the total number of possible outcomes will
be five and not six.

The probability of event A, with the condition that event B has happened will 2/5. This
conditional probability is denoted as P(A/B). Let us define the concept of conditional
probability in a formal manner.

Let A and B be any two events associated with a random experiment. The probability of
occurrence of event A when the event B has already occurred is called the conditional
probability of A when B is given and is denoted as P(A/B). The conditional probability
P(A/B) is meaningful

So far, we have assumed that the elementary events are equally likely and we have
used the corresponding definition of probability.

However the same definition of conditional probability can also be used when the
elementary events are not equally likely. This will be clear from the following example.

Suppose a die is tossed. Let B be the event of getting a perfect square.

Learn More On :- What is the Slope Formula
The die is so constructed that the event numbers are twice as likely to occur as the odd
numbers.

Let us find the probability of B given A, where A is the event getting a number greater
than 3 while tossing the die.

Conditional Probability Examples

Example 1 :- A card is drawn from an ordinary deck and we are told that it is red, what
is the probability that the card is greater than 2 but less than 9.

Solution :- Let A be the event of getting a card greater than 2 but less than 9.

B be the event of getting a red card. We have to find the probability of A given that B
has occurred. That is, we have to find P (A/B).

In a deck of cards, there are 26 red cards and 26 black cards.

\ n(B) = 26

Among the red cards, the number of outcomes which are favourable
Solving Math Problems
To solve Math problems quickly and accurately you need an understanding of various
math concepts and solving math problems is not an easy task.

TutorVista has a team of expert online Math tutors to help you understand Math
problems online and find out how to get solutions for them.

Our tutors work with you in learning basic to advanced topics. So we assure you
complete learning to solve math problems online.

Math Problems made Easy

One of the biggest problems in math that students encounter is solving word problems.
Word Problems occur in every topic and every grade.

Be it fractions, algebra, geometry or calculus, there are always word problems. Get
math problem solver online now. Try our free math problems online help demo and
interact with our expert math tutors. Students can check out the algebra word problems
page.
Solving Math problems is not easy! A lot of students have difficulty with Math questions.
But, employing some of these techniques will help you to solve Math problems easily :

The following steps are generally followed to solve Math problems:

Read it carefully - Math problem solving involves reading the problem slowly and
carefully, in order to understand what is to be solved. At times, you miss out important
information when you give it a quick reading.

Break the problem into parts - Before solving a problem, it is important to break it
down into parts. Clearly define what you need to do, what all information has been
given in the problem and what you already know. Once you have that written down, it
gets easier to solve the math problem online.

Change it into an equation - It is important to convert what you read in words into an
equation you can solve. So basically you need to change the English into numbers!

Always cross check - Once you get the answer to your Math problem, you should
always go back and recheck.

Sometimes, you might miss out on small details and going over the problem and
solution again helps.

Read More On :- Formula to Find Slope
Ask until it gets clear - Math is all about concepts. So, it is important to understand the
'process' of how to solve a Math problem, until you get around to doing it.

It is important to ask questions and get clarity on the concept. Once a new topic is
introduced, you should write it down, review it and in case of any doubts bring it up with

This process of continuously revising what you learn will gear you up to solve math
problems online.

Help with Math Topics

TutorVista's expert tutors will make solving problems very easy. Our expert tutors will
work with you in a personalized one-on-one environment to help you understand Math
questions better, thereby, ensuring that you are able to solve the problems.
College Algebra solvers help students to solve the word problems step by step. They
teach students how to understand the data given in the statement and solve for the
value to be found out.

The online Algebra tutors serve as free Algebra Solver who would help students in
interpreting the word problems. Let us go over a few important Math equivalents of
English for numbers and algebra word problems so as to make the interpretation of
word problems easier.

Add---- sum, total of, added to, together, increased by
Subtract-difference between, minus, less than, fewer than
Multiplication-of times, by a factor
Division-per, out of, ratio of, percent

The above words are suggestive of the operations associated with them. Students can
learn more in depth about them on understanding algebra word problems and tke the
help of online Algebra Solvers.
Thank You

TutorVista.com

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Description: When we are solving Conditional Probability Examples ,we deal with two events, say A and B , sometimes these events are so related to each other , that the probability will depend on whether the other event has already occurred. Conditional probability can be defined as the probability of an event given that another event has already occurred. Let’s consider an example for Conditional probability: Consider a card game, suppose a player needs to draw 2 cards of the same suit to win, out of 52 cards there can be 13 cards in each suit. If the first player draws a heart, and the player wishes to draw a second heart. If one heart has already been chosen, then we only have 12 hearts remaining out of 51 cards. So the conditional probability P = 12/51