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Fundamentals of Probability
Unit 7A Fundamentals of Probability Ms. Young
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Definitions Outcomes are the most basic possible results of observations or experiments. An event consists of one or more outcomes that share a property of interest. Ms. Young
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Expressing Probability
The probability of an event, expressed as P(event), is always between 0 and 1 (inclusive). A probability of 0 means the event is impossible and a probability of 1 means the event is certain. 1 0.5 Certain Likely Unlikely 50-50 Chance Impossible 0 ≤ P(A) ≤ 1 Meteorology offers a rich source of ideas here. Would you take an umbrella to work if the chance for rain is at 10%? How about 90%? Ms. Young
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Theoretical Method for Equally Likely Outcomes
Step 1: Count the total number of possible outcomes. Step 2: Among all the possible outcomes, count the number of ways the event of interest, A, can occur. Step 3: Determine the probability, P(A). Ms. Young
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Outcomes and Events Assuming equal chance of having a boy or girl at birth, what is the probability of having two girls and two boys in a family of four children? Of the 16 possible outcomes, 6 have the event two girls and two boys. P(2 girls) = 6/16 = 0.357 One of the challenges many students have with probability is knowing when to trust intuition and when to back away from it. Many students would answer the question with a 50%. This problem is a classic example of the importance of looking at the total number of outcomes. Ms. Young
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Empirical and Subjective Probabilities
An empirical probability is based on observations or experiments. It is the relative frequency of the event of interest. A subjective probability is an estimate based on experience or intuition. Ms. Young
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Three Types of Probabilities
Theoretical probability The chance of rolling a 4 is 1 out of 6. Empirical probability Subjective probability Ms. Young
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Three Types of Probabilities
Theoretical probability She’s a 92% free throw shooter for the season. Empirical probability Subjective probability Ms. Young
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Three Types of Probabilities
Theoretical probability There’s about a 70% chance she will go out on a date with me. Empirical probability Subjective probability Ms. Young
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Probability of an Event Not Occurring
If the probability of an event A is P(A), then the probability that event A does not occur is 1 – P(A). Since the probability of a family of four children having two girls and two boys is 0.375, what is the probability of a family of four children not having two girls and two boys? P(not 2 girls) = 1 – = 0.625 Ms. Young
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Making a Probability Distribution
A probability distribution represents the probabilities of all possible events. To make a probability distribution, do the following: Step 1: List all possible outcomes. Use a table or figure if it is helpful. Step 2: Identify outcomes that represent the same event and determine the probability of each event. Step 3: Make a table listing each event and probability. Ms. Young
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A Probability Distribution
All possible outcomes and a probability distribution for the sum when two dice are rolled are shown below. Possible outcomes Point out that the reason 7 is considered a lucky number in many gambling games is simply because there are more ways to roll a 7 than any other number. Ms. Young
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Odds Odds are the ratio of the probability that a particular event will occur to the probability that it will not occur. The odds for an event A are The odds against an event A are Ms. Young
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