{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Statistics_4_3

# Statistics_4_3 - Chapter 4 Probability and counting rules...

This preview shows pages 1–9. Sign up to view the full content.

Chapter 4: Probability and counting rules 4-1 Sample Spaces and Probability 4–2 The Addition Rules for Probability 4–3 The Multiplication Rules and Conditional Probability 4–4 Counting Rules 4–5 Probability and Counting Rules

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Sample Spaces and Probability A probability experiment is a chance process that leads to well-defined results called outcomes. An outcome is the result of a single trial of a probability experiment. A sample space, S, is the set of all possible outcomes of a probability experiment. Examples: .
Example : Find the sample space for rolling two dice. Solution: Example : Find the sample space for drawing one card from an ordinary deck of cards. Solution: .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example : Find the sample space for the gender of the children if a family has three children. Solution : BBB BBG BGB GBB GGG GGB GBG BGG A tree diagram is a device consisting of line segments emanating from a starting point and also from the outcome point. It is used to determine all possible outcomes of a probability experiment . Example, .
An event consists of a set of outcomes of a probability experiment . An event with one outcome is called a simple event . a compound event consists of two or more outcomes or simple events. There are three basic interpretations of probability: Classical Probability Classical probability assumes that all outcomes in the sample space are equally likely to occur. Equally likely events are events that have the same probability of occurring. .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Find the probability of getting a red ace when a card is drawn at random from an ordinary deck of cards. Solution: P (red ace)= g2870 g2873g2870 . Example: A card is drawn from an ordinary deck. Find these probabilities. a. Of getting a jack b. Of getting the 6 of clubs (i.e., a 6 and a club) c. Of getting a 3 or a diamond d. Of getting a 3 or a 6. Solution: a. P(jack)= g2872 g2873g2870 = g2869 g2869g2871 b. P (6 of clubs)= g2869 g2873g2870 c. P (3 or diamond)= g2869g2874 g2873g2870 = g2872 g2869g2871 d. P (3 or 6)= g2876 g2873g2870 = g2870 g2869g2871
Basic probability rules Probability Rule 1 The probability of any event E is a number between and including 0 and 1. This is denoted by 0 ≤ P ( E ) ≤ 1. Probability Rule 2 If an event E cannot occur (i.e., the event contains no members in the sample space), impossible event, Ø, its probability is 0. Probability Rule 3 If an event E is certain, E=S , then the probability of E is 1 or P(S)=1 . Probability Rule 4 The sum of the probabilities of all the outcomes in the sample space is 1.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The complement of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E. The complement of E is denoted by g1831 g3364 g1867g1870g1831 g3004 Example : Find the complement of the event E= Rolling a die and getting a 4 or 6. Solution: g1831 g3364 = {1,2,3,5) Complementary Events Rule: Example: If the probability that a person lives in an industrialized country of the world is g2869 g2873 , find the probability that a person does not live in an industrialized country.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern