School

University of MarylandDepartment

MathematicsCourse Code

MATH 011Professor

JarchowStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**3 pages of the document.**MATH111 Exam 2 Study guide

Key concepts covered:

I. Rules of probability

II. Use of counting techniques in probability

III. conditional probability and independent events

IV. Bayes Theorem

V. Distribution of random variables

VI. Expected Value

I. Rules of probability

1. properties of probability

1. Probability of event (E) is greater than or equal to 0 for any event

2. Probability of the total sample space (S) is equal to 1

3. If two separate events (E) or (F) are mutually exclusive, then the probability of their

union is equal to the sum of the probability of the two events

1. P(E U F) = P(E) + P(F)

4. Property three only applies if the events are mutually exclusive (no event E is included

in event F). The general case for two events is the addition rule. Which states that the

probability of the union of events E and F is equal to the sum of the two probabilities

minus the intersection

1. P(E U F) = P(E) + P(F) – P(E ∩ F)

5. The probability of the compliment of event E is 1 minus the probability of E

1. P(E^c) = 1 – P(E)

II. Use of counting techniques in probability

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