Definition of Probability

Introduction to Probability Definition:

In math, the probability is one of the important and very simple subjects. Generally the probability is defined as something will be happening. The probability contains sample space, events and experiments. The probability has many types; the two important types are Poisson distribution probability and binomial distribution. Now we will see the definition of probability. I like to share this Law of Probability with you all through my article.

Definition of probability:

Definition of  probability is a possible outcome of a particular process.The part of math that studies the possibility of incidence of random events in order to predict the actions of defined systems.The Probability is a method of expressing knowledge that an action will happen or has occurred.

Formula for Probability:

Probability =` ("Number of probable events")/ ("Total given events")` .

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Example 1:


In a class room 48 students are studying some subjects. In that class room 16 students are studying math subject, 12 students are studying physics subject and 20 students are studying biology subject.What is the probability for,

i. Select the Math students.

ii. Select the biology students.

Solution:

Step 1:

Given:

Total students n(S) = 48.

Studying math students n (A) =16.

Studying Physics students n (B) = 12.

Studying Biology students n(C) = 20.

Step 2:

i. Probability for getting math students:

P (event) = `("Number of favorable math students")/("Total students").`

Number of math students = 16.

Total students = 48.

= `16/48` .

=` 8/24` .

ii. Probability for selecting biology students:

Step 1:

P (event) = `("Number of favorable biology students")/("Total students").`

Here number of biology students = 20.

Total students = 48.

= `20/48`

=`5/12`


Example 2:


The three coins are flip at the same time. What is the probability of getting exacting two tails or three heads?

Solution:

The sample space, when three coins tossed is,

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

n(S) = 8

A be the event of exacting two tails,

n (A) = {HTT,THT,TTH,TTT} = 4

B be the event of getting exacting three heads,

n (B) = {HHH} = 1

P (A) =`4/8`

P (B) = `1/8`

P (A or B) = P (A) + P (B)

= `4/8` + `1/8` .

=` 5/8` .

= 0.63

The expected value in this probability model is 0.63.

The above information is the definition of probability.

Applied Probability

Introduction of applied probability:

Analysis of random situation, condition, or events is called Probability. Probability is the numerical analysis of impossibility to absolute certainty. Probability is the possibility that something will happen - how likely it is that some event will happen. For example, when picking a one card of diamond from the pack of 52 cards, the probability of picking a diamond card is 13/52, or 1/4.


Formulas for applied probability


Formula 1: Compliment

If AA and A'A' are complements then P(A) + P(A' ) = 1P(A)+P(A' )=1

Formula 2: Addition Rule

P(A OR B) = P(A) + P(B) - P(A AND B)P(A OR B)=P(A)+P(B)-P(A AND B)

Formula 3: Mutually Exclusive

If AA and BB are mutually exclusive then

P(A AND B) = 0P(A AND B)=0 ; so

P(A OR B) = P(A) + P(B)P(A OR B)=P(A)+P(B).

Formula 4: Multiplication Rule

P(A AND B) = P(B) P(A|B)P(A AND B)=P(B)P(A|B)

P(A AND B) = P(A) P(B|A)P(A AND B)=P(A)P(B|A)

Formula 5: Independence

If AA and BB are independent then:

P(A|B) = P(A)P(A|B)=P(A)

P(B|A)= P(B)P(B|A) =P(B)

P(A AND B) = P(A) P(B)

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Examples for applied probability:


Applied Probability Problem 1: A die is rolled, find the probability that an odd number is obtained.

Solution:

Let us first write the sample space S.

S = {1,2,3,4,5,6}
Let E be the event "an odd number is obtained" and write it down.

E = {1,3,5}
We now use the formula of the classical probability.

P(E) = n(E) / n(S) = 3 / 6 = 1 / 2
Applied Probability Problem 2: Two coins are tossed, find the probability that two tails are obtained.

Solution 2:

The sample space S is given by.

S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event "two tails are obtained".

E = {(T,T)}
We use the formula of the classical probability.

P(E) = n(E) / n(S) = 1 / 4

Three Types of Probability

Introduction to three types of probability:

Three types of probability article deals with the definition of three types of probability and the model problems related to it.

Types of probability:

The probability is classified in to

Probability as counting.
probability as geometry
Probability as algebra, are the three types and the explanation is given below

Three Types of Probability:

Probability as counting:

This probability is very simple and easy to understand. This is used to find the probability of number of times an event occurs. This probability is calculated by dividing the number of successive out come by the total number of outcomes.

Probability as counting =` (("number of sucessive outcome")/ ("total number of outcomes"))`

Probability as geometry:

This probability is suitable for one or more continuous variable. We can find the probability dividing the length of successive part by the length of total parts in the event.

Probability as geometry = `(("length of successive part")/ ("length of total part"))` .

Probability as algebra:

This is applicable to problems where we can find the enough relationship between two probabilities, at that time we can solve the problem algebraically.Having problem with 10 cbse sample papers keep reading my upcoming posts, i will try to help you.

Model Problems to three Types of Probability:

Problem 1: what is the probability of getting 5, when a dice is thrown?

Solution:

The sample space S = {1, 2, 3, 4, 5, 6}

n(S) = 6

Getting 5 = {5}

n (5)= 1

Probability of getting 5 = `(n (5))/(n(S))`

= `(1/6)`

Probability of getting 5 is `(1/6)` .

Problem 2:

The probability of getting mark in next test is x, which is likely, equal to three the marks he will not get.what is the probability of marks in next test.

Solution:

Getting mark in next test is x

Probability he will not get is 1-x

By given data:

x =2(1-x)

x= 2-2x

x+2x=2

3x =2

x=`2/3`

The probability of getting mark in next test is `2/3`

Problem 3:

John is working from 8am to 5pm, every 15minutes he will go out. What is the probability of going out from 4pm to 5pm?

Solution:

John goes out every 15 minutes.

Probability of going out from 4pm to 5pm = `(15minutes)/(60 minutes)`

= `(15/60)`

= `(1/4)`

Probability of going out from 4pm to 5pm is `(1/4)`