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Lecture 5
Calculating Probabilites Using Simple Events
Section 4.2 Calculating Probabilties using Simple Events
The probability of an event A is a measure of our believe that the event A will occur.
\[ P(A) = \lim_{n\to\infty} \frac{frequency}{n} \]
This is a limit of the relative frequency.
- \(P(A) = 0\)
- \(P(A) = 1\)
Each experiment results in one and only one single experiment. - Probabiliy of a single event must like between 0 and 1 - The sum of the probabilities for all simple events in S = 1.
If we can write down all simple events and find their individual probabilities, we can find the probability of an event A:
- The probability of an event A is equal to the sum of the probabilities of the simple events contained in A
Example 4.5
Toss two fair cons and record the outcome - find the probability of observing exactly one head.
What are the simple events? What is the probability of observing exactly one head?
Example 4.6
Proportinos of blood types A, B, AB and O in the Caucasian population in the US is .4, .11, .04, .45. What is the probability that a single Caucasian person chosen randomly will have either type A or type AB Blood?
\[ P(\text{A or AB}) = P(\text{A}) + P(\text {AB}) = 0.4 + .04 = .44 \]
Example 4.8
A candy dish contains one yellow and two red candies - close your eyes and choose two candies - what is the probability that both are red?
- Need to list all simple events via tree:
Homework
[1] "4.2.7-4.2.10, 4.2.27, 4.2.36"Answers: Chapter 4 - Section 2