Chapter%203

# Chapter%203 - Chapter 3 Probability In this chapter we will...

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1 Chapter 3 Probability In this chapter we will make the assumption that the population is known and answer questions about a sample based on the population information . Probability Examples: Plain M&M’s web site: http://us.mms.com/us/about/products/milkchocolate/ Birthday problem: Random Birthday Applet Graph of probabilities

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2 3.1 Events, sample spaces, and probability An experiment is the process of making an observation that cannot be predicted with certainty (the toss of the die) A sample point is the most basic outcome of an experiment An event is a specific collection of sample points. The sample space is the collection of all its sample points.
3 Example: What are the possible options (sample space) when flipping a coin? Tossing a die? Note: A die is a numbered cube with 6 sides represented by the numbers 1 – 6 Sample Space: 1 2 3 4 5 6 H or T

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4 Finding all sample points Determine how many smaller experiments are being conducted and always use a fixed structure – I use left to right structure Determine if each of the smaller experiments are independent from each other If there is independence, then each smaller experiment changes without affecting the other smaller experiments. If the smaller experiments are dependent, then take this into account when creating sample points.
5 Example: Coin Toss Sample Space One Coin Toss : (H) (T) Toss Two Coins : (H,H) (H,T) (T,H) (T,T) Toss Three Coins: (H,H,H), (H,H,T), (H,T,H), (H,T,T) (T,H,H), (T,H,T), (T,T,H), (T,T,T) Note: each flip is independent

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6 4 coin tosses Each toss is independent of the next and each side has the same probability of landing up Symbols of H (head) T (tail) and sample space point will be designated as (first, second, third, fourth) coin (H, H, H, H) (H, T, T, H) (T, H, T, T) (H, H, H, T) (H, T, T, T) (T, T, H, H) (H, H, T, H) (T, H, H, H) (T, T, H, T) (H, H, T, T) (T, H, H, T) (T, T, T, H) (H, T, H, H) (T, H, T, H) (T, T, T, T) (H, T, H, T)
7 Dice Throw 2 die (each is independent and each side has the same probability of landing face up Symbols of 1, 2, 3, 4, 5 and 6 will be used to represent dots and sample space point will be designated as (first, second) die side up (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) (1,2) (2,2) (3,2) (4,2) (5,2) (6,2) (1,3) (2,3) (3,3) (4,3) (5,3) (6,3) (1,4) (2,4) (3,4) (4,4) (5,4) (6,4) (1,5) (2,5) (3,5) (4,5) (5,5) (6,5) (1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

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8 Assigning Probabilities First need to know if each point in the sample space is equally likely to occur as all the other options (coin, die, card) or unequal possibility (having a disease, getting an A) If each possibility is equally likely, then the probability for each point is calculated as = 1/ number of sample space points If the sample space points do not have the same possibility of occurrence, then the probability for the points must be stated P(Disease) = 0.10
9 Properties of probabilities P( ) Symbol: P(A) is probability for event A General Properties of event probabilities

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Chapter%203 - Chapter 3 Probability In this chapter we will...

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