Question 1

A geneticist developed a new type of pest-resistant walnut tree. These walnut trees produce 75% of pest-resistant walnut trees and 25% of susceptible (not resistant) trees when two resistant trees are crossed. If two such trees are crossed, we will get:

Accepted Answer

A) a resistant tree every third crossing. 
B) a resistant tree for the first 70% of crossings and then susceptible trees. 
C) approximately 70% of resistant trees over many crossings. 
D) exactly 30% of susceptible trees over many crossings.

Question 2

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 exactly one red marble is given by:

Accepted Answer

A) 1/8. 
B) 3/8. 
C) 7/8. 
D) 1/3.

Question 3

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 random variable is:

Accepted Answer

A) the number of red marbles. 
B) the number of red, blue, or green marbles. 
C) the number of green marbles. 
D) None of the answer options is correct.

Question 4

I choose a card at random from a well-shuffled deck of 52 cards. There is a 1/4 probability that the card chosen is a spade, a 1/4 probability that the card is a heart, a 1/4 probability that the card is a diamond, and a 1/4 probability that the card is a club. Both spades and clubs are black cards, whereas hearts and diamonds are red. The probability that the card chosen is not a spade is:

Accepted Answer

A) 0.25. 
B) 0.5. 
C) 0.75. 
D) 1.

Question 5

You toss a thumbtack 100 times and observe that it lands point down 65 times. The proportion of times it landed point down is then 0.65. This proportion represents:

Accepted Answer

A) the sample proportion of tosses that landed point down in your 100 tosses. 
B) the correlation between the number of tosses and the number of times it landed point down. 
C) the variance of the number of point-down tosses. 
D) the probability that the thumbtack lands point down.

Question 6

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 undetermined. The probability of knowing that a tree from a crossing is at least somewhat resistant is:

Accepted Answer

A) P = 0.7. 
B) P = 0.4. 
C) P = 0.3. 
D) P = 0.1.

Question 7

According to the M&Ms Web site, each package of the milk chocolate candies typically contains 14% brown, 13% red, 14% yellow, 16% green, 24% blue, and 20% orange M&Ms. You go to the store and buy a standard package. When you open it, you find that it contains 51 M&Ms, distributed as follows.  The variable color is:

Accepted Answer

A) discrete. 
B) continuous. 
C) quantitative. 
D) None of the answer options is correct.

Question 8

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 Spanish is:

Accepted Answer

A) 0.08. 
B) 0.52. 
C) 0.48. 
D) The answer cannot be determined from the information given.

Question 9

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 undetermined. The probability of a tree from a crossing being not resistant or an unknown status is:

Accepted Answer

A) P = 0.2. 
B) P = 0.3. 
C) P = 0.4. 
D) P = 0.5.

Question 10

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. Some breeds of horses seem more prone to developing enteroliths than others. Below is a table with the distribution of enteroliths among the breeds.  The probability that a horse arriving at the veterinary hospital is not an Arabian or a quarter horse is:

Accepted Answer

A) 0.55. 
B) 0.25. 
C) 0.45. 
D) 0.75.

Question 11

The probability density of a random variable X is given in the following figure.  From this density, the probability that X is between 0.5 and 1.5 is:

Accepted Answer

A) 1/3. 
B) 1/2. 
C) 3/4. 
D) 1.

Question 12

A sample of horses admitted to a local veterinary hospital had the following distribution of mares, geldings, and stallions.  If we assume that the horses constitute a random sample of all horses in the state, then we estimate the probability that a randomly selected horse is a stallion to be:

Accepted Answer

A) 5.11. 
B) 0.511. 
C) 0.0511. 
D) None of the answer options is correct.

Question 13

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 by:

Accepted Answer

A)   
B)   
C)   
D)

Question 14

A random variable can be described as:

Accepted Answer

A) a probability of an event. 
B) a variable whose value is a numerical outcome of a random phenomenon. 
C) the proportion of times an event occurs over a long run of repeated trials. 
D) All of the answer options are correct.

Question 15

Horses are housed in pastures, pipe pens, or barn stalls at a local horse barn. Let X = the number of horses housed in barn stalls. Then X is:

Accepted Answer

A) a discrete random variable. 
B) a continuous random variable. 
C) an event. 
D) the sample space.

Question 16

A randomly selected sample of 100 horse owners found that 72 of them feed grass hay to their horses in the morning and alfalfa in the evening. The value 0.72 represents:

Accepted Answer

A) the probability that a randomly selected horse owner will feed grass hay in the morning and alfalfa in the evening. 
B) the proportion of horse owners in the sample that feed grass hay in the morning and alfalfa in the evening. 
C) the probability that a horse will be fed grass hay in the morning and alfalfa in the evening. 
D) All of the answer options are correct.

Question 17

A geneticist developed a new type of pest-resistant walnuts. These walnuts produce 75% of pest-resistant walnut trees and 25% of susceptible (not resistant) trees when two resistant trees are crossed. If a grower crossed 100 such pairs of trees for 100 offspring and did this many times over many years and plots, she should get:

Accepted Answer

A) approximately 70% of resistant trees over all plots and years. 
B) exactly 70% of resistant trees over all plots and years. 
C) exactly 70% of resistant trees in all plots and years. 
D) None of the answer options is correct.

Question 18

A North American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green. If you bet on red, the probability of winning is 18/38 = 0.4737. The probability 0.4737 represents:

Accepted Answer

A) the fact that you are more likely to win betting on red than you are to lose. 
B) the proportion of times this event will occur in a very long series of individual bets on red. 
C) the fact that if you make 100 wagers on red, you will have 47 or 48 wins. 
D) nothing important, because every spin of the wheel results in one of three outcomes (red, black, or green).

Question 19

A randomly selected sample of 100 horse owners found that 72 of them feed one flake of alfalfa plus one flake of grass hay in the evening to their horses, while the rest feed one flake of alfalfa plus oat hay in the evening. The estimated probability that horse owners feed alfalfa plus oat hay in the evening is:

Accepted Answer

A) 0.72. 
B) 0.5. 
C) 0.28. 
D) 0.75.

Question 20

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.  The probability of rolling a pair of 4s is:

Accepted Answer

A) 1/16. 
B) 1/8. 
C) 3/16. 
D) 13/16.

Exam 10: Introducing Probability

A geneticist developed a new type of pest-resistant walnut tree. These walnut trees produce 75% of pest-resistant walnut trees and 25% of susceptible (not resistant) trees when two resistant trees are crossed. If two such trees are crossed, we will get:

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 exactly one red marble is given by: