chapter5 - Chapter 5 Probability 5.1 Probability Rules 1...

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Chapter 5 Probability 5.1 Probability Rules 1. Empirical probability is based on the outcome of a probability experiment and is approximately equal to the relative frequency of the event. Classical probability is based on counting techniques and is equal to the ratio of the number of ways an event can occur to the number of possible outcomes in the experiment. 2. The probability of an impossible event is zero. No. An event with probability approximately zero is a very unlikely event, but it is not necessarily an impossible event. 3. Outcomes are equally likely when each outcome has the same probability of occurring. 4. An event is unusual if it has a low probability of occurring. The choice of a “cut off” should consider the context of the problem. 5. True 6. True 7. experiment 8. event 9. Rule 1 is satisfied since all of the probabilities in the model are greater than or equal to zero and less than or equal to one. Rule 2 is satisfied since the sum of the probabilities in the model is one: 0.3 + 0.15 + 0 + 0.15 + 0.2 + 0.2 = 1. In this model, the outcome “blue” is an impossible event. 10. Rule 1 is satisfied since all of the probabilities in the model are greater than or equal to zero and less than or equal to one. Rule 2 is satisfied since the sum of the probabilities in the model is one: 0 + 0 + 0 + 0 + 1 + 0 = 1. This model implies that all of the M&Ms in the bag are yellow. 11. This cannot be a probability model because P (green) < 0. 12. This cannot be a probability model because the sum of the probabilities is more than one: 0.1 + 0.1 + 0.1 + 0.4 + 0.2 + 0.3 = 1.2. 13. Probabilities must be between 0 and 1, inclusive, so the only values which could be probabilities are: 0, 0.01, 0.35, and 1. 14. Probabilities must be between 0 and 1, so the only values which could be probabilities are: 1 2 3 2 , , , 4 3 and 0. 15. The probability of 0.42 means that approximately 42 out of every 100 hands will contain two cards of the same value and three cards of different value. No. Just because 42 of the 100 hands are likely to contain a pair, this does not mean it will definitely happen. 16. The probability of 0.48 means that approximately 48 out of every 100 hands will contain two cards of the same value and three cards of different value. No. Just because 48 of the 100 hands are likely to contain a pair, this does not mean it will definitely happen. 265
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