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M316 Chapter 10

# A probability model is a mathematical description of

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Unformatted text preview: probabilities to events. A sample space can be very simple or very complex. When we toss a coin there are only two possible outcomes, heads and tails. The sample space can be represented by S = {H, T} . When Gallup draws a random sample of 1523 adults, the sample space contains all possible choices of 1523 of the 225 million adults in the country. This sample space is huge and each member is a possible sample (hence the term sample space). Example (10.4) Rolling Dice Many games of chance involve rolling two sixsided dice. Here are all the possible outcomes. Let A be the event that the total number of dots we see after a roll is 5. To determine its probability, we must assign a probability to each of the simple events (outcomes). We assume that the dice are "fair" which means that each outcome is equally likely. Since there are 36 mutually exclusive outcomes and their probabilities must add up to 1, each outcome must have a probability of 1/36. Since there are four mutually exclusive ways to roll a 5, the event A has probability 4/36. Example (10.5) Rolling Dice and Counting Spots Normally, we only care ab...
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