The surface of a circular dart board has a small center

Chapter 7, Problem 5.21

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The surface of a circular dart board has a small center circle called the bulls-eye and 20 pie-shaped regions numbered from 1 to 20. Each of the pie-shaped regions is further divided into three parts such that a person throwing a dart that lands in a specic region scores the value of the number, double the number, or triple the number, depending on which of the three parts the dart hits. If a person hits the bulls-eye with probability 0.01, hits a double with probability 0.10, hits a triple with probability 0.05, and misses the dart board with probability 0.02, what is the probability that 7 throws will result in no bulls-eyes, no triples, a double twice, and a complete miss once?

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