AMC 125: Lecture No. 1. Introduction to Probability Theory

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Link to blog post: http://raffysaldana.blogspot.com/2009/11/amc-125-lecture-no-1-introduction-to.html

AMC 125 – Mathematics for Computer Science II
Dr. Rafael P. Saldaña
Mathematics Department
School of Science and Engineering
Ateneo de Manila University
rsaldana@ateneo.edu


Lecture No. 1. A FIRST WORD ON PROBABILITY

Source: Grimaldi, 150 - 156.

TOPICS:

1. EXPERIEMENT

2. SAMPLE SPACE

3. DEFINITION OF PROBABILITY

Under the assumption of equal likelihood, let S be the sample space for an experiment E. Each subset A of S, including the empty subset, is called an event. Each element of S determines an outcome, so if S = n and a is an element of S, A is a subset of S, then

Pr({a}) = The probability that {a} (or, a) occurs = {a}/S, = 1/n, and

Pr(A) = The probability that A occurs = A/S = A/n

Note: We often write Pr(a) for Pr({a})

EXAMPLES:

1. When you toss a fair coin, what is the probability that you will get a head?

2. If you toss a fair die, what is the probability that you will get

(a) a 5?
(b) a 6?
(c) a 5 or a 6?
(d) an even number?
(e) an odd number?

3. There are 20 students enrolled in Dr. Saldana's class. If Dr. Saldana wants to select two of his students, at random, he may make a selection in (20 2) = 190 ways, so S = 190.

Suppose that Ace and Bob are two of Dr. Saldana's students in class.

Let A be the event that Ace is one of the students selected and B be the event that the selection includes Bob.

What is the probability that Dr. Saldana selects

a. Both Ace and Bob?

b. neither Ace nor Bob?

c. Ace but not Bob?



to be continued...

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