Discuss The Concept Of Probability

Discuss The Concept Of Probability, Including The Notion Of An Experiment, Outcomes, And Sample Space. How Can Each Of These Be Useful To Us?

Probability is a number that determines the chance or likelihood that a particular event will occur.  Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%. In this essay, I shall examine experiments whose results I cannot predict in advance. Such experiments are called Random Experiments. If I toss a coin, I may not be able to say for sure whether the coin will land with the head up or with the tail up. Similarly, if I toss a fair die, I am sure it will land but I am not sure which of the six faces will show up. The experiments of tossing a fair coin or a fair die are examples of random experiments. Probability is a branch of Mathematics dealing with random experiments.

Suppose I toss a fair coin 100 times, experience has shown that in most instances, the number of times a head shows up will be very close to 50. If I toss the coin 1000 times, the number of times a head shows up will also be very close to 500. If I denote the number of times we are successful in getting a head showing up by n(s) i.e. number of successes, and we denote the total number of trials by n(t), from empirical results, the ratio  becomes steady as the number of trials becomes large indefinitely. The ratio  defines the probability that a head shows up. The result is strictly empirical but it is very important, as it forms the basis of the theoretical work in probability.

SAMPLE SPACE AND EVENT SPACE

Any result of an experiment in probability is usually called an OUTCOME. If we cannot predict beforehand, the outcome of an experiment the experiment is called a RANDOM EXPERIMENT. The set of all possible outcomes of any random experiment will be called a SAMPLE SPACE and it will be denoted by S. The number of outcomes in S or the number of elements in the sample space will be denoted n(s).

A subset of the sample space which may be a collection of outcomes of a random experiment is called an EVENT SPACE. I will denote an event space by E and the number of outcomes or elements in E by n(E).

 The probability of an event E denoted Pr(E) is defined as    Pr(E) = 

Since the empty set  is a subset of the sample space n() = 0.    Pr() =  = 0

Pr() is the probability of an impossible event. Since s is a subset of itself. Pr() =  = 1

Pr(s) is the probability of an event which is certain to occur. The probability of an event E is, therefore, a number which satisfies the inequality 0 ≤ Pr(E) ≤1.

EXAMPLE

I was required to complete this specific task where I was to obtain a desired outcome of the task. A random sample of sixty candidates who sat for CCNA I and II of the CISCO examinations in a certain year is taken with the table that shows the number of candidates who passed or failed each part of the examination.

CCNA I

Total

Pass

Fail

CCNA II

Pass

Fail

20

35

Total

 

24

60

Completing the table, I answered these following questions and evaluated the ideal experiment outcome and sample space.

  1. If a candidate is chosen at random from the sample, use the table to find the probability that the candidate:
  • Passed CCNA I
  • Passed CCNA I and II
  • Passed CCNA II but failed CCNA I.
  1. If a candidate is chosen at random from the subgroup of those who failed CCNA I, find the probability that the candidate passed CCNA II.

SOLUTION

 

CCNA I

Total

Pass

Fail

 

CCNA II

Pass

 Fail

9

16

25

Total

24

36

60

i. let  be the event that a candidate chosen at random passed CCNA II.

            n() = 25;                   n(S)= 60

            Pr() =   =    =

  1. Let be the event that a candidate chosen at random passed CCNA I and II

             n() = 9;                   n(S)= 60

            Pr() =   =    =    

iii. Let  be the event that a candidate chosen at random passed CCNA II but failed CCNA I

             n() = 16;                   n(S)= 60

            Pr() =   =    =    

  1. If a candidate is chosen from a subgroup of those who failed CCNA I then the sample space has changed.

Let S’ be the new sample space:   n(S’) = 36.

Let  be the event that a candidate is chosen at random from a subgroup of those that failed CCNA I but passed CCNA II, n() = 16

             n() = 16;                   n(S’)= 36

            Pr() =   =    =    

Through the use of probability, I was able to solve the required task as a fraction and also as a percentage.

hihi

Download Sample Now

Earn back money you have spent on downloaded sample



Upload Document Document Unser Evaluion Get Money Into Your Wallet



Cite This work.

To export a reference to this article please select a referencing stye below.

Assignment Hippo (2021) . Retrive from http://www.assignmenthippo.com/sample-assignment/discuss-the-concept-of-probability

"." Assignment Hippo ,2021, http://www.assignmenthippo.com/sample-assignment/discuss-the-concept-of-probability

Assignment Hippo (2021) . Available from: http://www.assignmenthippo.com/sample-assignment/discuss-the-concept-of-probability

[Accessed 10/04/2021].

Assignment Hippo . ''(Assignment Hippo,2021) http://www.assignmenthippo.com/sample-assignment/discuss-the-concept-of-probability accessed 10/04/2021.


Want latest solution of this assignment

Want to order fresh copy of the Sample Template Answers? online or do you need the old solutions for Sample Template, contact our customer support or talk to us to get the answers of it.


+ Submit Your Assignment Here

Captcha Image

AssignmentHippo Features

On Time Delivery

Our motto is deliver assignment on Time. Our Expert writers deliver quality assignments to the students.

Plagiarism Free Work

Get reliable and unique assignments by using our 100% plagiarism-free.

24 X 7 Live Help

Get connected 24*7 with our Live Chat support executives to receive instant solutions for your assignment.

Services For All Subjects

Get Help with all the subjects like: Programming, Accounting, Finance, Engineering, Law and Marketing.

Best Price Guarantee

Get premium service at a pocket-friendly rate at AssignmentHippo

FREE SAMPLE FILE

Client Review

I was struggling so hard to complete my marketing assignment on brand development when I decided to finally reach to the experts of this portal. They certainly deliver perfect consistency and the desired format. The content prepared by the experts of this platform was simply amazing. I definitely owe my grades to them.

Tap to Chat
Get instant assignment help