Probability

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. 4GMAT'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 events.
5. Explanation of compound events
6. Method to evaluate the probability of an event with illustrative example and shortcut methods
7. 21 solved examples covering typical questions in tossing of coins, rolling of dice, picking cards from a pack of cards.
8. 15 exercise problems with the answer key and also explanatory answers
9. An objective type speed test with around 40 questions along with explanatory answers and answer key are provided for the speed test

Here is an example of a typical solved example in this chapter.
Sample Question
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?

Explanatory Answer
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 be orange = 6C4.

Probability: The probability that all four balls drawn are orange
=

Therefore, the probability that not all of the balls drawn are orange = 1 - probability of all four being orange
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