## Sunday, June 29, 2014

### Probability Basics : Lesson 1

Today we explore the basic concepts of Probability.

Probability is the measure of the likelihood of an "event" to occur.
For example, when we toss a fair coin, the chances of a head turning up are 1/2. When we roll a dice the chance of 2 appearing is 1/6.

### Important Terms:

1. Sample Space : The collection of all results is called the sample space of the event.
For example, when a coin is tossed, the Sample space(S) is the set {Head, Tails}.
When a dice is rolled, S = {1,2,3,4,5,6}

2. Event: A subset of the S is called an event. For example, when a coin is tossed, {Head}, {Tail} are events. Note that an event set can contain multiple items. For example when 2 coins are tossed, {Head,Head} is considered an event.

3. Equally Probable Events: When 2 events have the same likelihood of occuring, they are known as Equally Probable events. For example the chance of head and tails turning up on the toss of a coin are Equally Probable events.

### Probability

The Probability of an event occurring is defined as the number of cases favorable for the event divided by total number of events in the sample space.

If the event be called as 'A', the probability is represented as P(A)

Example: Probability that head shows up on tossing a coin
P(A) = Favorable Cases/Sample Space = 1/2

P(A') is used to represent the probability of event A not occurring.

Note: P(A) + P(A') = 1

If we have 2 events A,B as the overall sample space, then:

P(A) = A / (A+B) and P(B) = B / (A + B)

### Independent Events and Mutually Exclusive Events

A regular confusion among students is the difference between Independent and Mutually exclusive Events.

Let A, B be 2 events. P(A and B) = P (A ∩ B ) is defined as the probability that both A and B occur together.

For 2 independent events A, B, P(A ∩ B ) = P(A) * P(B)
For Mutually Exclusive events, P(A ∩ B ) = 0

This is best understood with an example.

Consider a fair coin and a fair six-sided die. Let event A be obtaining tails, and event B be rolling a 3. Then we can safely say that events A and B are independent, because the outcome of one does not affect the outcome of the other.

Here, P(A ∩ B ) = 1/2 * 1/6 = 1/12.
Here A and B are Independent Events (Not mutually exclusive).

Consider a fair six-sided dice, where even-numbered faces are colored red, and the odd-numbered faces are colored green. Let event A be rolling a green face, and event B be rolling a 6.

P(A) = 3/6 = 1/2
P(B) = 1/6

But note that A&B cannot occur simultaneously since 6 is always going to turn up on a red face.

Here, P(A ∩ B ) =0
Here A and B are Mutually exclusive events(Not independent).

In our next post we will go deeper into complex probability theory and solve a few problems and provide video solutions for the same.

## Monday, June 2, 2014

### CAT 2014: Registration, Syllabus and Format

The Common Admission Test 2014 (CAT 2014) is India's premier MBA entrance exam for admission into the 13 Indian Institutes of Managements. The CAT exam is conducted by the IIMs in a Computer Based Test (CBT) format once every year between October and November. Over 2 lakh candidates write the test from all over India. Apart from the IIMs, a number of other Indian institutes also consider CAT scores for admission.

### Who will be conducting it?

CAT 2014 will be conducted by a new test partner of the IIM's - TCS. The news was announced that TCS will be conducting CAT from 2014 to 2018.

### Has the registrations for CAT 2014 started?

Not Yet. Expect the advertisement in Mid July. Of course we will update this blog as and when the registrations begin.

### What is the Syllabus for CAT 2014?

The IIMs have never defined a syllabus for CAT but since it has always been an aptitutude test, the following is a good guide for the CAT syllabus.
• Quantitative ability
• Number Systems
• HCF, LCM
• Averages
• Percentages, Profit & Loss
• Simple/compound Interest
• Equations, Inequalities
• Complex numbers
• Functions
• Probability
• Permutation & Combination
• Mensuration
• Geometry
• Co-ordinate Geometry
• Trigonometry
• Set Theory
• Speed & Distance
• Work & Time
• Series & Progressions
• Surds & Indices
• Logarithms
• Ratio & Proportion
• Base Systems
• Data Interpretation
• Data Tables
• Pie Charts
• Line Graphs
• Bar graphs
• Other Chart types
• Data Sufficiency
• Verbal Ability
• Parajumbles
• Fill in the blanks
• Vocabulary
• Sentence Correction
• Analogies
• Meaning-Usage match
• Critical reasoning
• Facts/Inference/Judgment
• Logical reasoning
• Cubes & Dice
• Blood Relations
• Number & Letter Series
• Seating Arrangements
• Venn Diagrams
• Clocks & Calendars
• Analytical Reasoning
• Syllogism

### Format of the CAT 2014 Computer Based Test.

The CAT 2014 exam will contain 2 sections of 50 questions each.

Section1: Quantitative Techniques & Data Interpretation : 50 questions
Section2: Verbal Ability & Logical Reasoning : 50 questions
Total Time: 170 Minutes.