Section 3.1‚ Exercise #14‚ p. 125 Finding Probabilities consider a company that selects employees for random drug tests. The company uses a computer to select randomly employee numbers that range from 1 to 6296. Find the probability of selecting a number greater than 1000. P(E) = Number of outcomes in E / Total number of Outcomes in sample space Number of outcomes in E = 6296 – 100 = 5296 The probability = P(E) = 5296 / 6296 = 0.841 = 84.1%
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Unit 3 Tutorial Exercise Set 3A Calculating Probabilities Solutions can be found on page 6 1. Over a long period of time‚ the queue length of customers at the teller section of a major bank was observed to have the following probability distribution; Number in queue Probability 0 0.1 1 0.2 2 0.2 3 0.3 4 or more 0.2 Find the probability of a. At most two people in the queue. b. No more than three people in the queue. c. At least one person in the queue. d. Two or
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the difference between probability distributions and frequency distributions? Provide an example that demonstrates the difference between the two. A probability distribution directly corresponds to a frequency distribution‚ except that it is based on theory (probability theory)‚ rather than on what is observed in the real world (empirical data). A frequency distribution is based on actual observations. An example would be observing a coin be flipped twenty times. A probability distribution is theoretical
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However if you roll a one‚ then all the points you won that turn are lost. Content Probability is any fraction or percent going from 0 to 1. There are two types of probability; theoretical probability is the probability of what should happen. The theoretical probability of getting heads when flipping a coin is ½. The other kind of probability is observed probability. This is when you take the probability
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Table of Contents Introduction Cricket involves numbers‚ the comparison of these numbers will give us an idea regarding how well a team is faring. The comparison of these number widely depends on Statistics to give us a rational conclusion. Cricket is therefore a sport which involves a lot of statistics‚ Statistics are needed to determine the performance of a team in various formats such as one day‚ international. It is also needed to determine the performance
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find the probability of each of the events given in part b. 1) Probability of all three children having the same gender: P(BBB)= 1/8 P(GGG)= 1/8 P(BBB) + P(GGG)= 1/8 + 1/8 = 2/8 = 1/4 = .25 2) Probability of exactly two of the three children will be girls: P(BGG) + P(GBG) + P(GGB) = 1/8 +1/8 + 1/8 = 3/8 = .375 3) Probability of exactly one of the three children will be a girl: P(BBG) + P(BGB) + P(GBB) = 1/8 + 1/8 + 1/8 = 3/8 = .375 4) Probability that none of
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Chapter 3 – Problem 18 a) Let the probability of state 1 (the high performance state) be P(H) = 0.5 Let the probability of state 2 (the low performance state) be P(L) = 0.5 We assume that the amount of utility or satisfaction Ajay derives from a payoff is equal to the square root of the amount of the payoff. So‚ we get Ui(a) = √x‚ x≥0 Where x is the amount of the payoff The decision theory tells us that the act with the highest expected utility should be chosen. We denote
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successes in n trials Binomial Tables (in text) Problem • The probability that a patient recovers from a delicate heart operation is 0.9. What is the probability that exactly 5 of the next 7 patients having this operation survive? Negative Binomial Distribution k p k (1 p) p2 2 Note: Not in textbook Problem The probability that a patient recovers from a delicate heart operation is 0.9. • What is the probability that the 7th patient is the 5th patient to survive the operation? •
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answers at random. What is the probability that Mary will get a score of at least 30% on this exam? n=20‚ p=0.20 P(X≥6) (0.30)(20)=6 Distribution Plot Binomial‚ n=20‚ p=0.2 0.25 Probability 0.20 0.15 0.10 0.05 0.1958 0.00 0 P(X≥6)=0.196 X 6 If 40% is the lowest passing score‚ what is the probability that Mary will pass the exam? n=20‚ p=0.20 (0.40)(20)=8 P(X≥8) Distribution Plot Binomial‚ n=20‚ p=0.2 0.25 Probability 0.20 0.15 0.10
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|P(X = x) |X(P(X = x) | |0 |0.3 | | |1 |0.2 | | |2 | | | |3 |0.4 | | a. Find the probability that X = 2. b. Find the expected value. Exercise 2 Suppose that you are offered the following “deal.” You roll a die. If you roll a 6‚ you win $10. If you roll a 4 or 5‚ you win $5. If you roll a 1‚ 2‚ or 3‚ you pay $6. a. What
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