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The surface of a circular dart board has a small center circle called the bull's-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 on a specified number scores the value of the number, double the number, or triple the number, depending on which of the three parts the dart falls. 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?

According to a genetics theory, a certain cross of guinea pigs will result in red, black, and white offspring in the ratio 8: 4: 4 . Find the probability that among 8 offspring 5 will be red, 2 black, and 1 white.

The probabilities are \(0.4,0.2,0.3,\) and \(0.1,\) respectively, that a delegate to a certain convention arrived by air, bus. automobile, or train. What is the probability that among 9 delegates randomly selected at this convention, 3 arrived by air, 3 arrived by bus, 1 arrived by automobile, and 2 arrived by train?

Suppose that for a very large shipment of integrated-circuit chips, the probability of failure for any one chip is \(0.10 .\) Assuming that the assumptions underlying the binomial distributions are met, find the probability that at most 3 chips fail in a random sample of 20.

Assuming that 6 in 10 automobile accidents are due mainly to a speed violation, find the probability that among 8 automobile accidents 6 will be due mainly to a speed violation (a) by using the formula for the binomial distribution; (b) by using the binomial table.

If 7 cards are dealt from an ordinary deck of 52 playing cards, what is the probability that (a) exactly 2 of them will be face cards? (b) at least 1 of them will be a queen?

To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin pills that are similar in appearance. If the customs official selects 3 of the tablets at random for analysis, what is the probability that the traveler will be arrested for illegal possession of narcotics?

A homeowner plants 6 bulbs selected at. random from a box containing 5 tulip bulbs and 4 daffodil bulbs. What is the probability that he planted 2 daffodil bulbs and 4 tulip bulbs?

From a lot of 10 missiles, 4 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that (a) all 4 will fire? (b) at most 2 will not. fire?

A random committee of size 3 is selected from 4 doctors and 2 nurses. Write a formula for the probability distribution of the random variable \(X\) representing the number of doctors on the committee. Find \(P(2 \leq X \leq 3)\).