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Chapter 9: Problem 23
Find the probability for the experiment of drawing a card at random from a standard deck of 52 playing cards. The card is a red face card.
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Linear Model, Quadratic Model, or Neither? In Exercises \(61-68\) , write the first six terms of the sequence beginning with the given term. Then calculate the first and second differences of the sequence. State whether the sequence has a perfect linear model, a perfect quadratic model, or neither. $$a_{1}=0$$ $$a_{n}=a_{n-1}+3$$
American roulette is a game in which a wheel turns on a spindle and is divided into 38 pockets. Thirty-six of the pockets are numbered \(1-36,\) of which half are red and half are black. Two of the pockets are green and are numbered 0 and 00 (see figure). The dealer spins the wheel and a small ball in opposite directions. As the ball slows to a stop, it has an equal probability of landing in any of the numbered pockets. (a) Find the probability of landing in the number 00 pocket. (b) Find the probability of landing in a red pocket. (c) Find the probability of landing in a green pocket or a black pocket. (d) Find the probability of landing in the number 14 pocket on two consecutive spins. (e) Find the probability of landing in a red pocket on \(\quad\) three consecutive spins.
Graphical Reasoning In Exercises 83 and \(84,\) use a graphing utility to graph \(f\) and \(g\) in the same viewing window. What is the relationship between the two graphs? Use the Binomial Theorem to write the polynomial function \(g\) in standard form. $$f(x)=-x^{4}+4 x^{2}-1, \quad g(x)=f(x-3)$$
You are given the probability that an event will not happen. Find the probability that the event will happen. \(P\left(E^{\prime}\right)=\frac{61}{100}\)
Finding a Sum In Exercises \(45-54\) , find the sum using the formulas for the sums of powers of integers. $$\sum_{n=1}^{8} n^{5}$$
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