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

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

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