5.21 The surface of a circular dart board has a small center circle called the b

Question

5.21 The surface of a circular dart board has a small center circle called the bull's-eye and 20 pie-shaped re- gions 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 specific 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 bull's-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 bull's-eyes, no triples, a double twice, and a complete miss once?

Explanation / Answer

here probability of hitting a of bull's eye+double+triples+miss) =1-(0.01+0.1+0.05+0.02)=0.82

therfore probability of hitting no bull's eye, no triple a double twice and a complete miss=P( hitting 4 one ; 2 double and one complete miss) =(7!/(4!*2!*1!))*(0.82)4*(0.1)2*(0.02) =0.0095

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