elitmus aptitude tips

7/27/2019 Elitmus aptitude tips

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What is Probability and How to solve

Probability in Aptitute SectionProbability deals with the analysis of random phenomena. It is a way of assigning every event avalue between zero and one, with the requirement that the event made up of all possible results

is assigned a value of one.

2. Experiment

An operation which results in some well-defined outcomes is called an experiment.

Also Read:How to solve Logical reasoning part in Elitmus?

2.1. Random Experiment

An experiment whose outcome cannot be predicted with certainty is called a random

experiment. In other words, if an experiment is performed many times under similar conditions

and the outcome of each time is not the same, then this experiment is called a random

experiment.

Example:A). Tossing of a fair coinB). Throwing of an unbiased dieC). Drawing of a card from a well shuffled pack of 52 playing cards

3. Sample Space

The set of all possible outcomes of a random experiment is called the sample space for that

experiment. It is usually denoted by S.

Example:A). When a die is thrown, any one of the numbers 1, 2, 3, 4, 5, 6 can come up.Therefore, sample space:

S = {1, 2, 3, 4, 5, 6}
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B). When a coin is tossed either a head or tail will come up, then the sample space w.r.t. thetossing of the coin is:

S = {H, T}

C). When two coins are tossed, then the sample space is

3.1 Sample Point or Event PointEach element of the sample spaces is called a sample point or an event point.

Example:When a die is thrown, the sample space is S = {1, 2, 3, 4, 5, 6} where 1, 2, 3, 4, 5 and 6 are the

sample points.

3.2 Discrete Sample Space

A sample space S is called a discrete sample if S is a finite set.

4. Event

A subset of the sample space is called an event.

Also Read:How to solve Logical reasoning part in Elitmus?

4.1. Problem of Events

Sample space S plays the same role as universal set for all problems related to the particular

experiment.(i). is also the subset of S and is an impossible Event.(ii). S is also a subset of S which is called a sure event or a certain event.

5. Types of Events


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A. Simple Event or Elementary Event

An event is called a Simple Event if it is a singleton subset of the sample space S.

Example:A). When a coin is tossed, then the sample space isS = {H, T}

Then A = {H} occurrence of head and

B = {T} occurrence of tail are called Simple events.

B). When two coins are tossed, then the sample space isS = {(H,H); (H,T); (T,H); (T,T)}

Then A = {(H,T)} is the occurrence of head on 1st and tail on 2nd is called a Simple event.

B. Mixed Event or Compound Event or Composite Event

A subset of the sample space S which contains more than one element is called a mixed event

or when two or more events occur together, their joint occurrence is called a Compound Event.

Example:

When a dice is thrown, then the sample space is

S = {1, 2, 3, 4, 5, 6}

Then let A = {2, 4 6} is the event of occurrence of even and B = {1, 2, 4} is the event of

occurrence of exponent of 2 are Mixed events.

Compound events are of two type:

(i). Independent Events, and(ii). Dependent Events

C. Equally likely events


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Outcomes are said to be equally likely when we have no reason to believe that one is more

likely to occur than the other.

Example:

When an unbiased die is thrown all the six faces 1, 2, 3, 4, 5, 6 are equally likely to come up.

D. Exhaustive Events

A set of events is said to be exhaustive if one of them must necessarily happen every time the

experiments is performed.

Example:

When a die is thrown events 1, 2, 3, 4, 5, 6 form an exhaustive set of events.

Important: We can say that the total number of elementary events of a random experiment iscalled the exhaustive number of cases.

E. Mutually Exclusive Events

Two or more events are said to be mutually exclusive if one of them occurs, others cannot

occur. Thus if two or more events are said to be mutually exclusive, if not two of them can

occur together.

Hence, A1,A2,A3,,An are mutually exclusive if and only if AiAj=, for ij

Example:

A). When a coin is tossed the event of occurrence of a head and the event of occurrence of a tailare mutually exclusive events because we cannot have both head and tail at the same time.

B). When a die is thrown, the sample space is S = {1, 2, 3, 4, 5, 6}Let A is an event of occurrence of number greater than 4 i.e., {5, 6}

B is an event of occurrence of an odd number {1, 3, 5}


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C is an event of occurrence of an even number {2, 4, 6}

Here, events B and C are Mutually Exclusive but the event A and B or A and C are not Mutually

Exclusive.

F. Independent Events or Mutually Independent events

Two or more event are said to be independent if occurrence or non-occurrence of any of them

does not affect the probability of occurrence of or non-occurrence of their events.

Thus, two or more events are said to be independent if occurrence or non-occurrence of any of

them does not influence the occurrence or non-occurrence of the other events.

Example:Let bag contains 3 Red and 2 Black balls. Two balls are drawn one by one with replacement.Let A is the event of occurrence of a red ball in first draw.

B is the event of occurrence of a black ball in second draw.

Then probability of occurrence of B has not been affected if A occurs before B. As the ball has

been replaced in the bag and once again we have to select one ball out of 5(3R + 2B) given balls

for event B.

Also Read:How to solve Logical reasoning part in Elitmus?6. Occurrence of an Event

For a random experiment, let E be an event

Let E = {a, b, c}. If the outcome of the experiment is either a or b or c then we say the event has

occurred.

Sample Space: The outcomes of any typeEvent: The outcomes of particular type

6.1. Probability of Occurrence of an event

Let S be the same space, then the probability of occurrence of an event E is denoted by P(E) and

is defined as

P(E)=n(E)n(S)= number of elements in E number of elements in S

P(E)= number of favourable/particular cases total number of cases


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Example:A). When a coin is tossed, then the sample space is S = {H, T}Let E is the event of occurrence of a head

E = {H}

B). When a die is tossed, sample space S = {1, 2, 3, 4, 5, 6}Let A is an event of occurrence of an odd number

And B is an event of occurrence of a number greater than 4

A = {1, 3, 5} and B = {5, 6}

P(A) = Probability of occurrence of an odd number =n(A)n(S)

=36=12 and

P(B) = Probability of occurrence of a number greater than 4 =n(B)n(S)

=26=13

7. Basic Axioms of Probability

Let S denote the sample space of a random experiment.

1. For any event E, P(E)0

2. P(S)=1

3. For a finite or infinite sequence of disjoint events E1,E2,

P(E1E2E3)=iP(Ei)


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Simple way to solve calender problems in

Aptitude section

Most of the students are having difficulties in solving the Calendar problems.Already many logics are there to solve these kinds of problems, but all these logics are difficult

to understand. So here is the simple way to solve calendar problems. Also Read:How tosolve Logical reasoning part in Elitmus?In order to solve these type of problems you must know some codes.

Year Code Month Code Day Code

Year Code:-

1600-1699 61700-1799 4

1800-1899 2

1900-1999 0

2000-2099 4

Month Code:-

Jan Feb Mar April May June July Aug Sep Oct Nov Dec0 3 3 6 1 4 6 2 5 0 3 5Day Code:-

Sunday Monday Tuesday Wednesday Thursday Friday Saturday0 1 2 3 4 5 6Steps to solve:-

Step 1: Add the day digit to last two digit of the year.Step 2: Divide the last two digits of the year by four.Step 3: Add the Quotient value in step 3 to result obtain in step 1.Step 4: Add Month Code and year codes to the result obtain in step3.Step 5: Divide the result ofstep4 by seven.Step 6: Obtain the remainder and match with the day code.
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Simple way to solve clock based problems in

Aptitude Section

Clock based problems are one of the frequently asked questions in most of the competitive

exam. To solve these problems, it is always better to understand some of the basic principles and

the types of problems that get asked. In this post I hereby explained simple tricks and some

simple formulas for solving clock based problems.

In every competitive exams clock questions are categorized in to two ways.

Problems in angles Problems on incorrect clocks

Problems in angles

Method :1

Before we actually start solving problems on angles, we need to know couple of basic factsclear:

Speed of the hour hand = 0.5 degrees per minute (dpm) Speed of the minute hand = 6 dpm At n o clock, the angle of the hour hand from the vertical is 30n

The questions based upon these could be of the following types

Example : 1

What is the angle between the hands of the clock at 7:20At 7 o clock, the hour hand is at 210 degrees from the vertical.In 20 minutes,Hour hand = 210 + 20*(0.5) = 210 + 10 = 220 {The hour hand moves at 0.5 dpm}Minute hand = 20*(6) = 120 {The minute hand moves at 6 dpm}Difference or angle between the hands = 220 120 = 100 degrees

Method : 2

Example :2

Find the reflex angle between the hands of a clock at 05.30?The above problem are solved by the bellow formulaAngle between X and Y =|(X*30)-((Y*11)/2)|

Angle between hands at 5:30Step 1: X=5 , Y=30Step 2: 5*30=150Step 3: (30*11)/2 = 165Step 4: 165-150=15


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Thus, angle between hands at 5:30 is 15 degrees.

Method : 3

Example : 3

At what time 3&4o clock in the hands of clock together.

Approximately we know at 03:15 hands of the clock togetherSo 15*60/55=16.36 min

Problems on incorrect clocks

Such sort of problems arise when a clock runs faster or slower than expected pace. Whensolving these problems it is best to keep track of the correct clock.

Example : 4

A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it showat 10 PM on the same day?The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

Important Notes

Two right angles per hour(Right angle = 90, Straight angle=180) Forty four right angles per day Between every two hours the hands of the clock coincide with each other for one

time except between 11, 12 and 12, 1.In a day they coincide for 22 times. Between every two hours they are perpendicular to each other two times except

between 2, 3 and 3, 4 and 8, 9 and 9, 10.In a day they will be perpendicular for 44

times. Between every two hours they will be opposite to each other one time except

between 5, 6 and 6, 7.In a day they will be opposite for 22 times.

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