9: Probability
- Page ID
- 155315
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9-1 Determining Probabilities
9-2 Multistage Experiments and Modeling Games
9-3 Simulations and Applications in Probability
9-4 Permutations and Combinations in Probability
Chapter 9 Review
- 9.1: Basic Concepts
- If you roll a die, pick a card from deck of playing cards, or randomly select a person and observe their hair color, we are executing an experiment or procedure. In probability, we look at the likelihood of different outcomes.
- 9.2: Working with Events
- Now let us examine the probability that an event does not happen. As in the previous section, consider the situation of rolling a six-sided die and first compute the probability of rolling a six: the answer is P(six)=1/6. Now consider the probability that we do not roll a six: there are 5 outcomes that are not a six, so the answer is P(not a six)=5/6.
- 9.3: Bayes' Theorem
- In this section, we concentrate on the more complex conditional probability problems we began looking at in the last section.
- 9.4: Counting
- You already know how to count or you wouldn’t be taking a college-level math class, right? Well yes, but what we’ll be investigating here are ways of counting efficiently. When we get to the probability situations a bit later in this chapter, we will need to count some very large numbers, like the number of possible winning lottery tickets. One way to do this would be to write down every possible set of numbers that might show up on a lottery ticket, but believe me: you don’t want to do this.
- 9.5: Expected Value
- Expected value is perhaps the most useful probability concept we will discuss. It has many applications, from insurance policies to making financial decisions, and it’s one thing that the casinos and government agencies that run gambling operations and lotteries hope most people never learn about.
- 9.6: Exercises
- This page contains 89 exercise problems related to the material from Chapter 10.
- 9.7: Probability
- Probability is always a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain. The probabilities in a probability model must sum to 1. See Example. When the outcomes of an experiment are all equally likely, we can find the probability of an event by dividing the number of outcomes in the event by the total number of outcomes in the sample space for the experiment.