A bridge hand has been dealt. Are the following two conditional probabilities equal? If a given hand has an ace, what is the probability that the given hand has a second ace? Given that the hand has...
A bridge hand has been dealt. Are the following two conditional probabilities equal? If a given hand has an ace, what is the probability that the given hand has a second ace? Given that the hand has...
Pr[A]=13 Pr[A1]=112 Pr[A2]=14 Pr[1|B]=12 Pr[2|B]=12 Pr[B1]=16 Pr[B2]=16 Pr[C1]=112 Pr[C2]=14 Find the following missing probabilities: (1) Pr[1|A]= (2)...
A student takes a multiple-choice exam. Suppose for each question he either knows the answer or gambles and chooses an option at random. Further suppose that if he knows the answer, the probability...
Of a group of children, 0.4 are boys and 0.6 are girls. Of the boys, 0.7 have brown eyes; of the girls, 0.4 have brown eyes. A child is selected at random from the group. (a) Find the probability...
In a second-semester English class, 40% of the students are sophomores and the rest freshmen; 25% of the sophomores are repeating the course and 15% of the freshmen gained admission to the course...
A card is drawn from a pack of 52 playing cards. Find the probability that the card will be a king, given that it is a face card. (The face cards are the jacks, queens, and kings. Enter your probability...
involving drawing calculators from a box of working and broken calculators. Assume that the box contains 14 calculators: 12 that work and 2 that do not work. A sample of 3 calculators is selected...
Assume that the machine yields the item selected 70 percent of the time, and returns nothing 30 percent of the time. Three individuals attempt to use the machine. Let X be defined as the number of...
involving the selection of two students from a committee of students. Assume that the committee is made up of 2 males and 5 females. Two are selected at random, and a random variable X is defined...
Assume that the drawer contains 12 coins: 3 quarters, 5 dimes, and 4 nickels. One coin is randomly selected. What is the expected value of the coin selected (in cents)?
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...
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...
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 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...
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)...
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 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...
Assume that 40 percent are of type A, 20 percent of type B, and 40 percent of type C. It is known that 30 percent of seeds of type A, 60 percent of type B, and 70 percent of type C have germinated...
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 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...