Exam 10: Introducing Probability

Suppose we roll two fair four-sided dice. Let X denote the sum of the two roll outcomes. For example, if the first roll yields 3 and the second roll yields 1, then X = 3 + 1 = 4. The probability distribution for X is given below. P(X < 5) has the value:

A randomly selected sample of 100 horse owners found that 72 of them feed two flakes of grass hay in the morning and one flake of alfalfa plus one flake of grass hay in the evening to their horses. The estimated probability that horse owners feed grass hay in the morning and alfalfa plus grass hay in the evening is:

An urn contains 2 red and 2 green marbles. We pick a marble, record its color, and replace it. We repeat this procedure a second and a third time. The probability distribution for the number of red marbles is given below. For this distribution, the probability of 2 or more red marbles is given by:

A geneticist is conducting research on pest-resistant walnut trees. He has developed a set of trees, when crossed, to produce offspring as follows: 50% of all trees are very resistant, 30% of trees are somewhat resistant, and 20% are susceptible to invasion by pest. The probability model for the experiment of crossing two trees from the set of trees is:

An urn contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the number of red marbles in the 4 picks, the probabilities associated with this experiment are P(0) = 0.24, P(1) = 0.41, P(2) = 0.265, P(3) = 0.076, and:

A geneticist is conducting research on pest-resistant walnut trees. He has developed a set of trees, when crossed, to produce offspring as follows: 40% of all trees are very resistant, 30% of trees are somewhat resistant, and 20% are susceptible to invasion by pest, for the rest susceptibility status is unknown. Which of the following is a valid probability for an experiment of crossing two trees from his set?

You randomly select 500 students and observe that 85 of them smoke. What is your estimate of the probability that a randomly selected student smokes?

A fair dice is rolled and the sample space is given as S = {1, 2, 3, 4, 5, 6}. Which of the following statements is true?

A geneticist is conducting research on pest-resistant walnut trees. He has developed a set of trees, when crossed, to produce offspring as follows: 50% of all trees are very resistant, 30% of trees are somewhat resistant, and 20% are susceptible to invasion by pest. The probability that a tree will be at least somewhat resistant is:

An assignment of probabilities to events in a sample space must obey which of the following?

An urn contains 3 red, 2 blue, and 5 green marbles. If we pick 4 marbles with replacement and count the number of red marbles in the 4 picks, the sample space is given by which of the following?

The amount of milk sold each day by a grocery store varies according to the Normal distribution with mean 130 gallons and standard deviation 12 gallons. On a randomly selected day, the probability that the store sells at least 154 gallons is:

At a small college, all entering freshmen must take a foreign language class, chosen from the languages Spanish, French, Swahili, Chinese, and Arabic. Because there is limited space in the foreign language courses, a student cannot simultaneously enroll in more than one course. The probability distribution for the language studied by a randomly selected freshman is summarized in the following table. The probability that the freshman is studying Chinese or Swahili is:

A basketball player makes 70% of her free throws. When fouled, she gets to take two free throws. Let X represent the number of free throws made in two tries. The probability distribution for the number of free throws she makes in two attempts is summarized in the following table. The probability that she makes at least one free throw is:

An arborist is commissioned to study the amount of tree decay in a forest. The arborist obtains detailed information about the forest, the location, the annual rainfall, the type of tree species and other plants present, the pests and insects associated with tree death, and other information deemed relevant. On the basis of this information, the arborist reports that she puts the proportion of decayed trees at 22%. Therefore, she concludes that the probability of a randomly selected tree having decay is p = 0.22. This is an example of:

According to the Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups: If we randomly select a full-time student, what is the probability that the student is 25 or older?

A North American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green. Suppose you decide to bet on red on each of 10 consecutive spins of the roulette wheel. Suppose you lose the first five wagers. Which of the following is true?

The management for a chain of restaurants recorded the number of appetizers, X, ordered by tables dining. They observed that X had the following probability distribution. The probability that a randomly chosen table orders at least one appetizer is:

According to the Current Population Survey, the following table summarizes probabilities for randomly selecting a full-time student in various age groups: If we randomly select a full-time student, the probability that the student is 20-34 years old is:

Every year, the veterinary hospital at a major research university treats a number of horses that have stones called enteroliths in their guts. A sample of 20 years shows that, on average, about 2% of horses presenting at the veterinary hospital are treated for enteroliths. In the long run, the probability that a horse arriving at the veterinary hospital has enteroliths is: