about the professor who sometimes forgets to bring her briefcase to the office, but assume that, each day, the probability that she forgets the briefcase is 1/6. Assume that her forgetting is a Bernoulli...
about the professor who sometimes forgets to bring her briefcase to the office, but assume that, each day, the probability that she forgets the briefcase is 1/6. Assume that her forgetting is a Bernoulli...
100 people were asked if they knew who any of the following are: Thor, Zeus, and Osiris. 25 people did not know any of these. 3 people knew all three. 48 people knew who Zeus or Osiris...
events A and B of a sample space S, but assume that Pr[A] = 0.35 and Pr[B] = 0.5. Find Pr[A∪B] under each of the following conditions: (1) If A ⊂ B, then Pr[A∪B] = . (2)...
Assume that you have 10 mice in the cage: 4 white males, 3 gray females, and 3 gray males. Two mice are selected simultaneously and at random, and their colors are noted. What is the probability...
Assume that the box contains 2 defective widgets and 10 acceptable widgets. There are 4 inspectors, each of whom selects a widget from the box at random, inspects it, and then replaces it in the box...
Assume that each bag contains 5 balls. Bag a contains 3 red and 2 white, while bag b contains 1 red, 3 white, and 1 blue. You randomly select one ball from bag a, note the color, and place the ball...
involving the rolling of two fair dice. Answer the following questions. (1) What is the probability that the sum is 11, given that at least one of the numbers rolled is even? (2) What...
about a multiple-choice test in which each question has 4 choices only one of which is correct. Assume that 9 questions are answered by guessing randomly. What is the probability of getting exactly...
Assume that the business makes a profit with probability 0.3 in the first year. For each year thereafter, the business makes a profit with probability 0.6 if it made a profit in the previous year,...
involving a student's attendance at math and accounting classes on Mondays. Assume that the student attends math class with probability 0.65, skips accounting class with probability 0.25, and attends...
about independent events A and B in a sample space S, but assume that Pr[A] = 0.25 and Pr[B] = 0.3. Compute the following conditional probabilities: (1) Pr[A | B] = (2)...
involving weights of outcomes in a sample space S = { O1, O2, O3, O4 }. Assume that Pr[ { O1, O2 } ] = 0.51, Pr[ { O1, O3 } ] = 0.56, and Pr[ { O1, O2, O3 } ] = 0.77. Find the associated weights for...
independent events E and F in a sample space S, but assume that Pr[E] = 0.4 and Pr[F] = 0.15. Compute the following conditional probabilities: (1) Pr[E′| F] = (2) Pr[E...
For this problem, assume that Pr[A ∪B] = 0.6 and Pr[A] = 0.35. (1) What is Pr[B] if A and B are independent events? (2) What is Pr[B] if A and B are disjoint events?
Assume that your sample space is S = { O1, O2, O3, O4, O5 } with associated weights (probabilities) w1 = 0.15, w2 = 0.30, w3 = 0.20, w4 = 0.10, and w5 = 0.25. Determine the probability of the following...
For this problem, assume the box contains 3 red balls, 5 blue balls, and 8 white balls, and that we choose two balls at random from the box. What is the probability of neither being red given...
Assume that you have 5 red balls and 6 blue balls from which randomly to select two without replacement. (1) What is the probability that exactly one blue ball is chosen? (2) What is...
For this problem, assume there are 5 grey females, 2 grey males, 4 white females, and 5 white males. As in the book, the biologist selects two mice randomly. (1) What is the probability of selecting...
For this problem, assume that the committee contains 10 men and 5 women and that three are selected at random for a subcommittee. What is the probability that the subcommittee consists of 2 men...
Assume that you have 6 red balls and 7 blue balls from which randomly to select two without replacement. (1) What is the probability that exactly one blue ball is chosen? (2) What is...