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# Probability Theory

Probability theory is concerned with analyzing random phenomena such as dice rolls, coin flips, and slot machines. It is the basis of the mathematical field of statistics. Probability theory considers both discrete and continuous events. An example of a question concerning discrete events would be: “Heads or tails?” An example of a question concerning continuous events would be: “What time will the train arrive?”

Probability theory starts by considering a sample space of an event. A sample space is simply the set of all possible outcomes. For example, for a fair die, when rolled, the sample space is {1, 2, 3, 4, 5, 6}. Probability is simply assigning each of these events in the sample space a value between zero and one, with the whole sample space's probabilities summing to one. The probability indicates the likelihood of an event. In this case, each event has the same probability of one sixth.

Furthermore, the law of large numbers is a theorem that has risen from this basic foundation of probability theory. The law of large numbers simply states that as a sample grows larger and larger, the average result will converge towards the expected outcome of the probability distribution. In this case, it would mean that as you roll the dice more and more times, the running average will approach three and a half.

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### MATH 123: Probability

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### Simple Probability Questions

Consider a container filled with balls in a variety of colors. The bar graph below represents the number of balls of each color in the container. Red Green Yellow Blue Orange Purple Brown 2. If you select one ball randomly from the container (No Peeking!), what is the likelihood that it will be orange? Answer as percent ro

### The Unfair Die

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### Probability Questions 3A

1. The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. About 68% of all pregnancies last between a. 250 and 282 days b. 234 and 298 days c. 218 and 314 days d. 250 and 266 days 2.

### Probability Questions 2A

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