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chapter1solutions - 3 a The probability if winning can be...

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STAT 230 Solutions to Problems: Chapter 1 1. The probability of winning a lottery can be obtained by the “classical” definition: every combination is equally likely, so the probability that you will win (with one ticket) is ) (# 1 tickets possible . The probability that a bus will be late coming to your stop can be estimated by the “relative frequency” method, since over time you will have a good idea of how likely it is to arrive on time based on past experience. The probability that you will get caught speeding is estimated by the “subjective probability” method. 2. a) Relative frequency – based on your past experience. For example, if you’ve had 2 claims in 10 years you could estimate the probability as 0.2 = 1/5 b) Subjective probability, since it’s unlikely that there has ever been a meltdown of that type of reactor in the past. Also since a meltdown is an unpredictable event, there’s no way of modeling when it will happen. c) Classical definition: Its 1/12 assuming all days are equally likely as birthdays.
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Unformatted text preview: 3. a) The probability if winning can be determined exactly (although the very low result doesn’t seem to deter people!) b) Usually they do NOT audit every item in every statement. Instead, likely using a relative probability only a subset is audited. If you want to cheat, you must face the fact that there is a probability you will be caught and realistically you can only estimate that probability subjectively, since the auditors are unlikely to reveal what model they use. c) The probability that a given individual will catch a disease can be estimated very accurately using relative frequencies. d) Consider a simple poll like “Will you vote for X or Y?” Since poll-taking methodology usually takes great care to truly randomly select individuals, we can assume every person is equally likely to be selected. Thus you can calculate how accurate a poll is using this “fact”....
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