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Probability

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WORD POWER

Experiment:An operation which can produce some well-definedoutcomes is called an experiment.Random Experiment:

An experiment in which all possible outcomes are know andthe exact output cannot be predicted in advance, is called arandom experiment.Examples:

Rolling an unbiased dice.Tossing a fair coin.

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Sample Space:

When we perform an experiment, then the set Sof all possible outcomes is called the samplespace .

Examples:n tossing a coin, S ! "#, T$f two coins are tossed, the S ! "##, #T, T#, TT$.n rolling a dice, we have, S ! "%, &, ', (, ), *$.

Event:An+ subset of a sample space is called an event .

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PROBABILITY:Probabilit is the measure of the likeliness that

an event will occur. Probabilit is uantified as anumber between and % where indicates

impossibilit+ and % indicates certaint+/. Thehigher the probabilit of an event, the more

certain we are that the event will occur.PROBABILITY: n!mber o" "avorable o!tcomes

Total n!mber o" o!tcome

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Important DetailsWhen we throw a coin, then either a #ead #/ or a Tail T/

appears

A dice is a solid cube, having * faces, marked %, &, ', (, ), *respectivel+. When we throw a die, the outcome is the numberthat appears on its upper face.

A pack of cards has )& cards.t has %' cards of each suit, name Spades# $l!bs# %earts and

Diamonds .

0ards of spades and clubs are blac& cards .0ards of hearts and diamonds are red cards .There are 'in(s# )!eens and *ac&s . These are all called "acecards .

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Res!lts on Probabilit :•

P(S) = 1• 0

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1roblem uestions

1' An nbiased die is tossed '*nd the+robability o$ ,ettin, a - lti+le o$ .'

A'1/B'1/.

'0

2'343E 4F 56E AB47E

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2&. Three unbiased coins are tossed. What is the

probabilit+ of getting at most two heads3

A.'456. )450.%457.845

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2'. Two dice are thrown simultaneousl+. What is the probabilit+ of getting two numbers whose product iseven +

A.' 4(6.%%4'*0.&'4'*7.%4(

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2(. n a lotter+, there are % pri9es and &) blanks. A

lotter+ is drawn at random. What is the probabilit+ ofgetting a pri9e3

A. %48

6. &480. '487. (48

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2). :rom a pack of )& cards, two cards are drawn

together at random. What is the probabilit+ of both thecards being kings3

A.%4&&%6.)4&&%0.84&&%7.;

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2*. A bag contains & red, ' green and & blue balls. Two balls are drawn at random. What is the probabilit+ thatnone of the balls drawn is blue3A.%'4&%

6.%%4&%0.% 4&%7.;

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28. n a class, there are %) bo+s and % girls. Three

students are selected at random. The probabilit+ that% girl and & bo+s are selected, is

A.&)4%%86.%4)0.&%4(*7.'4&)

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25. Two cards are drawn at random from a pack of

)& cards. what is the probabilit+ that either both are black or both are ueen.

A.''%4%'&*6.))4&&%0.%%4%'&*7.;

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2?. A bag contains * white and ( black balls. & balls

are drawn at random. :ind the probabilit+ that the+are of same color.

A. 84%)

6. 54%)0. %4)7. (4)

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2% . A card is drawn from a pack of )& cards. The

probabilit+ of getting a ueen of club or a king ofheart is@

A.%4)&6.&4%'0.%4&*7.%4%'

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2%%. Two cards are drawn together from a pack of )&

cards. The probabilit+ that one is a spade and one is aheart, is@

A.'4&6.%'4% &0.(84&7.&?4'(

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2%&.

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2%'. A man and his wife appear in an interview for

two vacancies in the same post. The probabilit+ ofhusbandCs selection is %48/ and the probabilit+ ofwifeCs selection is %4)/. What is the probabilit+ thatonl+ one of them is selected 3

A.'4 (6.&480.(4)7.%48

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2%(. 5wo brother 8 and 9 a++eared $or an

e a-' 5he +robability o$ sele;tion o$ 8 is1/ and that o$ B is />' Find the+robability that both o$ the- are sele;ted'

A. %4?6. &4?0. %4*'7. &4*'

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2%). n a class, ' D of the students offered =nglish,

& D offered #indi and % D offered both. f a studentis selected at random, what is the probabilit+ that he.has offered =nglish or #indi

A.E6.F0.&4)7.(4)

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1 ' #$ two letters are ta?en at rando- $ro-the word 64@E& what is the +robabilitythat none o$ the letters wo ld be vowels

A'B'C

'1/.

2'1/

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