# Math Book 3: Probability

Discrete probability. Independent events. Mutually exclusive events.

Probability questions tested in the GMAT quant section include concepts such as independent events, exclusive events, exhaustive events, complimentary events, and questions covering tossing coins, and rolling dice.

### Concepts Covered

The concepts in this topic are essentially an extension of the fundamentals learnt in Permutation Combination. Many of the probability questions are restricted permutation questions. Wizako's GMAT Math Lesson Book in this chapter covers the following concepts:

1. Introduction to the concept of probability
2. Meaning of sample space and events along with illustrative examples to explain the same
3. Types of experiments in probability
4. Introduction to independent events, mutually exclusive events and probability of complimentary and exhaustive events.
5. Explanation of compound events
6. Method to evaluate the probability of an event with illustrative example and shortcut methods
7. Geometric probability
8. 6 illustrative examples. 27 solved examples covering typical questions in tossing of coins, rolling of dice, picking cards from a pack of cards.
9. 13 exercise problems with the answer key and also explanatory answers
10. An objective type test with 45 GMAT level multiple choice questions in the work book. An answer key and explanatory answer for all questions is provided.

Here is a typical solved example from this chapter.

### Sample Question

A bag contains 5 yellow balls and 6 orange balls. When 4 balls are drawn at random simultaneously from the bag, what is the probability that not all of the balls drawn are orange?

Sample Space (Denominator) : Four balls can be drawn from a bag containing 11 balls in 11C4 ways

Event (Numerator) : The number of ways in which all four balls drawn will all be orange = 6C4.

Probability: The probability that all four balls drawn are orange
= $\frac {{^{6}}{C}_{4}} {{^{11}}{C}_{4}}$ = $\frac {30} {330}$ = $\frac {1} {11}$

Therefore, the probability that not all of the balls drawn are orange = 1 - probability that all four are orange
= 1 - $\frac {1} {11}$
= $\frac {10} {11}$

### Chapterwise details of Wizako's Math Lesson Books

Math Lesson Book 1

 1 Linear Equations Details 2 Quadratic Equations Details 3 Set Theory Details 4 Sequences & Series Details 5 Number Properties & Theory Details 6 Inequalities Details 7 Functions

Math Lesson Book 2

 1 Descriptive Statistics Details 2 Ratio Proportion Details 3 Mixtures 4 Interest 5 Rates: Speed Distance Details 6 Rates: Races Details 7 Rates: Work Time Details

Math Lesson Book 3

 1 Percents Details 2 Profits Details 3 Permutation Combination Details 4 Probability Details 5 Geometry Details 6 Solid Geometry 7 Coordinate Geometry Details