chapter 3 notes

# chapter 3 notes - STA 2023 Elementary Statistics Lecture...

This preview shows pages 1–4. Sign up to view the full content.

STA 2023 Elementary Statistics Lecture Notes Chapter 3 – Probability Professor Achenbach Probability Probability is a mathematical measure of the likelihood of an event occurring. Probabilities are always fractions or decimals indicating the portion or percent of the time that the event occurs. Examples: 40% chance of rain Batting Average of .313 The probability of a royal flush is 1:649,740 Interpretations: A 40% chance of rain means that if we look at all days with similar conditions, 40% of those days had rain. A batting average of .313 means that the player got a base hit in 31.3% (.313) of his attempts at bat. On average, a royal flush will be dealt once for every 649,740 hands of poker. Probability Experiments A probability experiment is any process whose result is determined by chance. Examples: Roll a die. Flip a Coin. Draw a card from a shuffled deck Choose a name from a hat. 1

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

View Full Document
Outcome – Any possible result of a probability experiment. Sample Space – The collection of all possible outcomes for an experiment. The sample space is often denoted by S . Examples: The sample space of the experiment Flip a Coin has 2 outcomes heads and tails, so we could write: {heads, tails} S = The experiment of rolling a die has 6 possible outcomes 1-6, so: {1,2,3,4,5,6} S = Note: Each outcome for an experiment completely describes the outcome of the experiment. Event – Any collection of outcomes from the sample space. We will generally use capital letters to represent events. Examples: Rolling an even number is an event for the experiment of rolling a die. If we call this event E , we could write: {2,4,6} E = Drawing a king is an event for the experiment of drawing a card from a deck. If we call this event K , then K contains 4 outcomes: king of hearts, king of spades, king of diamonds and king of clubs. An event E for an experiment is said to have occurred if the outcome of the experiment is one of the outcomes of E. Example: If E is the event described above, and if when the die is cast, a 4 is showing, then we would say that E occurred. If a 1 was rolled, then E did not occur. 2
Calculating the Probability of an Event The probability of an event E is denoted by ( ) P E and always represents the fraction (or percentage) of trials of the experiment on which E occurs. Note: For any event E : 0 ( ) 1 P E . An event E is called impossible if ( ) 0 P E = . An event E is called certain if ( ) 1 P E = . ( ) P E can be calculated in two different ways: Empirical Probability Empirical Probability – A probability calculated by collecting data from past trials of the experiment. The probability obtained is then used to predict the future likelihood of the event occurring. Examples:

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 16

chapter 3 notes - STA 2023 Elementary Statistics Lecture...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online