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There are 4 married couples attending a party. Two identical door prizes are randomly awarded to two different people.
Answer the following questions. (Give your answers correct to three decimal places.)
(a) What is the probability one prize goes to a man and one to a woman?
(b) What is the probability a married couple wins both of the prizes?
(c) John and Mary are one of the married couples at the party. If Mary wins a prize, what is the conditional probability that John will win the other prize?
(d) If Mary does not win a prize, then what is the conditional probability that John will win one of the two prizes?
You have 80 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Let phi : R^2 --> R be a function given by phi(x,y) = x^3 + xy + y^3 +1 For which points p =(0,0) , p=(1/3,1/3), p =(-1/3,-1/3) is the subset phi^-1 ( phi(p)) an imbedded sub-manifold of R^2.
Find all the subfield of K containing Q.
You are given the choice of three doors. Behind one is a new car and the others hide a barnyard animal for you to keep. After you choose door number one, your host (Monty) opens door three to reveal a goat
What is the probability that he obtains a four -digit number less than 3265? A child takes four of the card and places them in some order.
Suppose that you flip a coin 10 times. What is the probability that you achieve at least 6 tails?
Find an equation for the planet's orbit. (Place the origin at the center of the orbit with the sun on the x-axis.
Law of sines.
A representative is to be selected from each of 3 departments in a small college. There are 7 people in the first department, 5 in the second department, and 4 in the third department.
You are the process improvement manager and have developed a new machine to cut insoles for the company's top-of-the-line running shoes. You are excited because the company's goal is no more than 3.4 defects per million
Find the equation of the circle with center at the intersection of 4x + y - 4 = 0 and x - y - 6 = 0 and passing through (-1, -3). What is the equation of the circle passing through (12, 1) & (2, -3) and having its center on the line 2x - 5y + 10 = 0..
Probability: Joint Probability Mass Function, Covariance and Variance Let X and Y have joint probability mass function Pr{X = i, Y = j}= c(i + 1)(j + 2) for i >= 0, j >= 0, and i + j
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