------------------------------------------------- Stats: Probability Rules "OR" or Unions Mutually Exclusive Events Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint. If two events are disjoint‚ then the probability of them both occurring at the same time is 0. Disjoint: P (A and B) = 0 If two events are mutually exclusive‚ then the probability of either occurring is the sum of the probabilities of each occurring. Specific
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What is the probability that at least two students were born on the same day of the year? For simplify the math‚ without changing the result significantly‚ let’s assume that year is always 365 days long (no February 29 birthdays) and let’s assume that a person has an equal chance of being born on any day of the year‚ although some birthday may be slightly more likely than others. If the students are 366 the probability would be equal to 1. If there is just 1 student the probability would be
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Statistics – Lab Week 4 Name: MATH221 Statistical Concepts: * Probability * Binomial Probability Distribution Calculating Binomial Probabilities * Open a new MINITAB worksheet. * We are interested in a binomial experiment with 10 trials. First‚ we will make the probability of a success ¼. Use MINITAB to calculate the probabilities for this distribution. In column C1 enter the word ‘success’ as the variable name (in the shaded cell above row 1. Now in that same column
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to the probability of actually earning less than the expected return – the greater the chance of low or negative returns‚ the riskier the investment. Investors take on higher risk investments in expectation of earning higher returns. Of course taking risk also means that the investor does not guarantee that the investment will be recovered. 3. PROBABILITY AND PROBABILITY DISTRIBUTION Probability – is the percentage chance that an event will occur. It range between 0 and 1.0. Probability Distribution
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TREE DIAGRAMS AND BINOMIAL PROBABILITIES (Chapter 20) Example 2 405 Self Tutor John plays Peter at tennis. The first to win two sets wins the match. Illustrate the sample space using a tree diagram. If J means “John wins the set” and P means “Peter wins the set” then the tree diagram is: 1st set 2nd set 3rd set J J J P P J We could write the sample space in set notation as S = fJJ‚ JPJ‚ JPP‚ PJJ‚ PJP‚ PPg. J P P P 2 Use a tree diagram to illustrate the sample space for the following:
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Question 1 1. The manager of Queensland Health’s computer network constructed the probability distribution for the number of interruptions to the system per day using historical data: Interruptions per day | 0 | 1 | 2 | 3 | 4 or more | Probability | 0.39 | 0.31 | 0.1 | 0.09 | ? | Determine the probability that on a given day there are more than two interruptions to the system. (2 decimal places) 2 points Question 2 1. The mean and standard deviation of a binomial distribution
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finding strategies for several different probability games. The key ideas were developed in the unit through the presentation of many games and variations of those games to us. The key ideas helped us to solve the central problem by giving us many opportunities to learn how to solve strategies for probability games. In each different game there was a new game or variation in which we could find a new way to find optimal game strategies for probability games. Why I chose each item: Homework
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A die is rolled‚ find the probability that an even number is obtained. Question 2: Two coins are tossed‚ find the probability that two heads are obtained. Question 3: Which of these numbers cannot be a probability? a) -0.00001 b) 0.5 c) 1.001 d) 0 e) 1 f) 20% Question 4: Two dice are rolled‚ find the probability that the sum is a) equal to 1 b) equal to 4 c) less than 13 Question 5: A die is rolled and a coin is tossed‚ find the probability that the die shows an odd number
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DESCRIPTIVE STATISTICS & PROBABILITY THEORY 1. Consider the following data: 1‚ 7‚ 3‚ 3‚ 6‚ 4 the mean and median for this data are a. 4 and 3 b. 4.8 and 3 c. 4.8 and 3 1/2 d. 4 and 3 1/2 e. 4 and 3 1/3 2. A distribution of 6 scores has a median of 21. If the highest score increases 3 points‚ the median will become __. a. 21 b. 21.5 c. 24 d. Cannot be determined without additional information
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Probability Introduction The probability of a specified event is the chance or likelihood that it will occur. There are several ways of viewing probability. One would be experimental in nature‚ where we repeatedly conduct an experiment. Suppose we flipped a coin over and over and over again and it came up heads about half of the time; we would expect that in the future whenever we flipped the coin it would turn up heads about half of the time. When a weather reporter says “there is a 10% chance
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