chapter3 acct

chapter3 acct - Chapter 3 Probability 3.1 Events, sample...

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1 Chapter 3 Probability 3.1 Events, sample space, and probability Basic definitions: An ______________ is an act of observation that leads to a single outcome that cannot be predicted with certainty. A _______________ (or simple event) is the most basic outcome of an experiment. _______________ (denoted S) is the collection of all possible outcomes of an experiment. An ______________ is a specific collection of sample points. Examples: 1. Experiment : toss a coin and observe the up face. Sample points : ______________ Sample space: _____________ Event A: head observed ____________ 2. Experiment: toss a die and observe the up face. Sample points : ____________ Sample space: _____________ Event A: even # observed ____________ Event B: # observed at least 3 _______________ 3. Experiment : toss two coins and observe the up faces. Sample space: S: _________________ Event A: at least one head observed _________________ 4. Experiment : toss three coins and observe the up faces. Sample space: S: __________________________________________________ Event A : at least one tail observed A: __________________________________________ 5. Experiment: Weather forecast (sunny, cloudy, rain) Sample space: ________________________ Event A : it won’t rain today. ___________________ Venn diagram: The ______________ of a _______________: measures the likelihood that the outcome will occur for a large number repetition.
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2 Law of Large Numbers : As a procedure is repeated over and over again, the relative frequency of an event tends to approach the true probability for that event. For example, throw a fair coin 10 times and 10000 times. Compare the P(H) and P(T). 10 times, for example, 4 heads, 6 tails, then P(H) = _____ P(T) = ______ 10000 times, for example, 4900 heads, 5100 tails, then P(H) = _____ P(T) = _____ So you can understand why we define the true P(H) = P(T) = ________ for a fair coin. Probability rules for sample points: Let i p represent the probability of sample point i, 1. All sample point probabilities must lie between 0 and 1: ___________ 2. The probabilities of all the sample points within a sample space must sum to 1: ___________ Find the probabilities for each sample point. Sample space: S: { } , HT Sample space: S: { } 1, 2, 3, 4, 5, 6 Sample space: S: { } ,,, HH HT TH TT The ______________of an ______________ is calculated by summing the probabilities of the sample points in the sample space for A. Event A: toss a die and observe an even number, _____________ So P(A) = So in the long run, you will win $1 with _______.
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3 Example1 . Nobel Prize Winner: A frequency distribution for the number of Nobel Prize winners (459) in science by country, for the years 1901-1999 are as follow. Country # of winners United States 199 United Kindom 71 Germany 61 France 25 Soviet Union 10 Japan 4 Other countries 89 Suppose a recipient of a Nobel Prize in science between 1901-1999 is selected at random. Find the probability that the Nobel Laureeate is from a. United States b. either France or Germany. c. any country other than Japan.
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4 Example2. 1. List all the possible outcomes when a couple has three children. S: {_____________________________________________} 2. Find the probability of event A that a couple has three children at least two boys. Define event A: three children at least two boys A: {______________________________} 3. Find the probability of event B that a couple has three children at least one girl.
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chapter3 acct - Chapter 3 Probability 3.1 Events, sample...

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