9394949438

[LATEST]$type=sticky$show=home$rm=0$va=0$count=4$va=0

Probability

Probability means the chance or occurrence of an event.
P (Occurrence of an event) =
For an event A is sure to occur, P(A) = I
For an event A is sure not to occur, P(A) = 0
For any event, 0 < P (A) < I

Sample Space: It is defined in the context of a random experiment and denotes the set representing ail the possible outcomes of the random experiment, [e.g. Sample space when a coin is tossed is (Head, Tail). Sample space when a dice is thrown is (1, 2, 3,4,5, 6).

Mutually Exclusive Events: A set of events is mutually exclusive when the occurrence of any one of them means that the other events cannot occur. (If head appears on a coin, tail will not appear and vice versa.)

Equally Likely Events: If two events have the same probability, or chance of occurrence they are called equally likely events. (In a throw of a dice, the chance of I showing on the dice is equal to 2 is equal to 3 is equal to 4 is equal to 5 is equal to 6 appearing on the dice.)

Exhaustive Set of Events : A set of events that includes all the possibilities of the sample space is said to be an exhaustive set of events, (e.g. in a throw of a dice the number is less than three or more than or equal to three.)

Independent Events: An event is described as such if the occurrence of an event has no effect on the probability of the occurrence of another event, (If the first child of a couple is a boy, there is no effect on the chances of the second child being a boy.)

Expectation: The expectation of an individual is defined as
Probability of winning × Reward of winning.

1. Additional Law of Probability:
For two events A and B
P (A or B) = P (A) + P (B) – P (A and B)
If the events are mutually exclusive
P(A and B) = 0

2. Multiplication Law of Probability:
If the events A and B are independent
P(A and B) = P(A) × P(B)

3. Complement of an event:
P(A°) = I – P (A)

Example 1 Find the probability that a leap year chosen at random will have 53 Sundays.
Solution: A leap year has 366 days = 52 weeks + 2 days
2 days can be (Sun-Sat, Sun-Mon, Mon-Tue, Tue-Wed, Wed-Thurs, Thurs-Fri, Fri-Sat)
P (53 Sundays) =

Example 2 3 coins are tossed together. Find the probability of getting
i) Exactly one head
ii) At least one head
iii) At most I head
Solution: Total number of cases when three coins are tossed together = 23 = 8. Now we will solve each of the above question one by one.
i) The cases of exactly one head are {(HTT)(TTH)(THT)}
Probability of getting exactly one head = 3/8
ii) Probability of getting atleast one head = I - probability of getting no head = 1 - (1/8) = 7/8
iii) The cases of at most one head {(TTT)(HTT)(TTH)(THT)}
. Probability of getting at most one head = 4/8 = 1/2

Example 3: Three unbiased coins are tossed. What is the probability of getting at least 2 heads? 
Solution: P (at least 2 heads) = P (2 heads) + P (3 heads)
2 heads = {(H, H, T), (H, T, H), (T, H H)}
3 heads = {(H, H, T)}
P (at least 2 heads) =

Example 4: An urn contains 9 red, 7 white and 4 black balls. If two balls are drawn at random. Find the probability that both the balls are red?
Solution:Total no of balls = 9-1-7 + 4 = 20
no. of ways of selecting 2 balls = 20C2
no. of ways of selecting 2 balls from 9 red balls = 9C2
P (Both red) =

Example 5: The letters of the word LUCKNOW are arranged among themselves. Find the Probability of always having NOW in such words.
Solution: Required Probability = =

Want to Know More
Please fill in the details below:

INNER POST ADS

Name

admit-card,10,Allegation,1,Alphabetical Series,3,Anagrams,1,Analogies,3,Answer Key,4,answer-key,1,Average,1,Blood Relation,2,CDP,33,Child Development,39,Child Development Pedagogy,33,Child Pedagogy,39,Cistern,1,Clock Calendar,4,Cloze Test,7,Coding Decoding,3,Compound Interest,1,CTET,325,ctet application form,1,CTET Coaching,2,ctet coaching centre delhi,1,ctet coaching in delhi,1,CTET Coaching in Dwarka,1,CTET Coaching in New Seemapuri,1,ctet exam study material,1,ctet examination pattern,1,ctet previous paper,1,ctet previous year solved paper,1,CTET Question Papers,1,CTET QUIZ,32,ctet study material,1,ctet study material for maths and science,2,ctet study material in english,1,CTET-2017,1,Cut Off,5,Data Interpretation,1,Development Process,1,Dice Test,1,Direction Sense Test,2,Distance,1,Download kvs Syllabus,1,DSSSB,187,DSSSB Coaching,6,DSSSB Exam,2,dsssb exam syllabus,1,dsssb study material,1,dsssb study material pdf,1,DSSSB Teachers,5,dsssb teachers eligibility criteria,1,DSSSB Teachers Selection,1,Education,1,Educational Psychology,5,Eligibility,1,English,24,English Grammar,3,English Pedagogy,10,English-Pedagogy,19,Environment,1,EVS Pedagogy,12,EVS-Pedagogy,6,EXAM,1,Exams,3,Featured,8,Forgetting,1,General Science-Biology,1,Geometry,1,Grammar,2,Guest Teachers,1,Hall Ticket,1,Heights & Distance,1,Heredity,1,Hindi,3,Idioms,3,Imp-Tips,4,Intelligence,1,job alerts,1,Jumbled Sentences,2,KVS,93,kvs exam pattern for pgt english,1,kvs online recruitment 2018,1,kvs syllabus 2019,1,kvs syllabus pgt hindi,1,kvs syllabus primary teacher,1,kvs teacher recruitment 2018,1,kvs tgt maths syllabus,1,kvs tgt pgt recruitment 2018,1,Latest Articles,150,Latest-Articles,1,Learning,1,Maths Pedagogy,10,Memory,1,Mensuration,1,Mixture,1,Mock test,33,MOCK TEST-DSSSB QUIZ,1,Motivation,1,NCF,104,Notification,21,Notifications,1,Number Puzzle,2,Number Series,3,Number System,1,Other Pedagogy,5,Partnership,1,Percentage,1,Permutation Combination,1,Personality,1,PGT,2,Pipes,1,Probability,1,Profit Loss,1,Progression,1,PRT,4,Psychology,2,Quant,17,Quant Notes,4,Quantitative Aptitude,17,Question Paper,1,Quiz,116,Ratio Proportion,1,Reasoning,30,Religious-Social,1,Results,8,Revision of the Day,15,Science Pedagogy,10,Seating Arrangement,3,Simple Interest,1,Speed,1,Spelling,3,SST Pedagogy,10,SST- Geography,12,SST-Civics and Economics,12,SST-History,27,study material for dsssb exam,1,Study Notes,79,Syllabus,18,Syllogism,2,Teachers Vacancies,2,TGT,1,Time,1,Vacancy,1,Venn Diagram,3,Verbal Ability,24,Vocabulary,3,Work,1,
ltr
item
DSSSB, CTET & KVS Exam Preparation | Clear CTET: dsssb-quants-probability-theory-part1
dsssb-quants-probability-theory-part1
https://2.bp.blogspot.com/-apyKszub4RQ/XBDw_E2wbWI/AAAAAAAADC4/tD0GHnnm8xclCezE1bspRTh_Wpr7Tk2xwCLcBGAs/s1600/quants-probability.jpg
https://2.bp.blogspot.com/-apyKszub4RQ/XBDw_E2wbWI/AAAAAAAADC4/tD0GHnnm8xclCezE1bspRTh_Wpr7Tk2xwCLcBGAs/s72-c/quants-probability.jpg
DSSSB, CTET & KVS Exam Preparation | Clear CTET
https://www.clearctet.com/2018/12/dsssb-quants-probability-theory-part1.html
https://www.clearctet.com/
https://www.clearctet.com/
https://www.clearctet.com/2018/12/dsssb-quants-probability-theory-part1.html
true
5140436504468951946
UTF-8
Loaded All Posts Not found any posts VIEW ALL Readmore Reply Cancel reply Delete By Home PAGES POSTS View All RECOMMENDED FOR YOU LABEL ARCHIVE SEARCH ALL POSTS Not found any post match with your request Back Home Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sun Mon Tue Wed Thu Fri Sat January February March April May June July August September October November December Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec just now 1 minute ago $$1$$ minutes ago 1 hour ago $$1$$ hours ago Yesterday $$1$$ days ago $$1$$ weeks ago more than 5 weeks ago Followers Follow THIS CONTENT IS PREMIUM Please share to unlock Copy All Code Select All Code All codes were copied to your clipboard Can not copy the codes / texts, please press [CTRL]+[C] (or CMD+C with Mac) to copy