Chapter 4
In a particular game, a ball is randomly chosen from a box that contains three red balls, one green ball, and six blue balls. If a red ball is selected, you win $2, if a green ball is selected you win $4, and if a blue ball is selected you win nothing. Let x be the amount that you win. The expected value of x is
$1
In a town, 30% of the households own a dog, 20% own a cat, and 60% own neither a dog nor a cat. If we select a household at random, the chance that they own both a dog and a cat is
.10
Parking on campus is often expensive, and it is tempting to park illegally and take your chances on getting a ticket. From past experience, the probability of getting a ticket is about 0.30 on any given day, and because you always change your parking location, each day's outcome is independent of the previous day's outcome.The probability that you will NOT get a ticket on two days is
.49
In a small town, 60% of the households have a pet dog. If a household has a pet dog, there is a 70% chance that the household also owns a cat. If a household does not have a dog, there is a 30% chance that the household owns a cat. What is the probability that a randomly selected household owns a cat?
.54
A shipment of computers received by a retailer consisted of the following configurations of hard drives with 80 or 120 gigabyte, and with 2 or 4 gigabytes of memory.A single computer is selected at random from the shipment.Let A be the event that the computer has a hard drive with 80 gigabytes.Let B be the event that the computer has a hard drive with 120 gigabytes.Let C be the event that the computer has 2 gigabytes of memory.Let D be the event that the computer has 4 gigabytes of memory.What is the conditional probability P(C|B)?
.73
A psychology instructor asked the 100 females in her class to rate their intelligence on a scale of 1 to 10. Some of the ratings were What proportion of the students rated their intelligence less than 5?
0
The variance of any fixed number a is ______.
0
The weight of medium-sized oranges selected at random from a large bin of oranges at the local supermarket is a random variable with mean µ = 12 ounces and standard deviation = 1.2 ounces. The weight of the oranges, in pounds (1 pound = 16 ounces) is a random variable with standard deviation
0.075 pounds
Suppose that about 20% of students in school have used marijuana in the last year. In order to preserve anonymity during surveys, a technique called randomized response is often used. A student is approached and asked to flip a coin but not show it to the interviewer. If the coin is heads, the student answers the question: "Was your mother born in January to June (inclusive)?" If the coin is tails, the student answers the question: "Have you used marijuana in the last year?" Because the interviewer does not know the outcome of the coin flip, the students' responses are confidential. What is the probability then that if a yes is received, the student used marijuana in the last year?
0.29
Let the random variable x be a random number with the uniform density curve given below.P (0.7 < x < 1.1) has value
0.30
Most people think babies are equally likely to come as either a boy or a girl. This is not true. Actually, about 51.3% of all babies are boys. If a family has two children (not twins), what is the chance they have one boy and one girl?
0.50
People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least one of them is a universal donor?
0.53
Females in a certain class rated their intelligence with a mean of 6.5. The males in the same class rated their intelligence with a mean of 7.25. The difference in the mean ratings (male -female) was
0.75
Suppose X is a continuous random variable taking values between 0 and 1 and having a probability distribution described by the following density curve.The probability that X takes a value between 0 and 3/4 is
0.875
Consider two events: E and F. We know that P(E) = P(F) = 0.7. Suppose we know that P(F|E) = 0.9. What is P(E|F)?
0.9
The weight of a medium size orange selected at random from a large bin of oranges at the local supermarket is a random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. Suppose we independently pick two oranges at random from the bin. The expected value of the sum of the weights of the two oranges, in pounds (1 pound = 16 ounces) is
1.5
A psychology instructor asked the 100 females in her class to rate their intelligence on a scale of 1 to 10. The ratings were The variance of the intelligence scores is
1.66
The weight of a medium-sized orange selected at random from a large bin of oranges at the local supermarket is a random variable with mean µ = 12 ounces and standard deviation = 1.2 ounces. Suppose we independently pick two oranges at random from the bin. The difference in the weights of the two oranges selected (the weight of the first orange minus the weight of the second orange) is a random variable with standard deviation
1.70 oz
Females in a certain class rated their intelligence with a mean of 6.5 with standard deviation 1.12. The males in the same class rated their intelligence with a mean of 7.25, with standard deviation 1.50. The standard deviation of the difference in the ratings (male - female) was
1.87
A fair coin is tossed, and a fair six-sided die is rolled. Suppose the outcomes for the coin and die are independent. The probability of getting a head and rolling a 6 is
1/12
A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. Imagine you stick your hand into the refrigerator and pull out a piece of fruit at random. What is the probability you pick a plum?
1/4
Most people think babies are equally likely to come as either a boy or a girl. This is not true. Actually, about 51.3% of all babies are boys. If a family has two children (not twins), what is the chance both children are boys?
26.3%
A fourth grade teacher gives homework every night in both mathematics and language arts. The time to complete the mathematics homework has a mean of 10 minutes and a standard deviation of 3 minutes. The time to complete the language arts assignment has a mean of 12 minutes and a standard deviation of 4 minutes. The time to complete the mathematics and the time to complete the language arts homework has a correlation ρ = -0.75. The standard deviation of the time to complete the entire homework assignment is
3 minutes
Suppose we have a loaded die which gives the outcomes 1 through 6 according to the probability distribution Note that for this die all outcomes are not equally likely as they would be if this were a fair die. If this die is rolled 6000 times, then , the sample mean of the number of spots on the 6000 rolls, should be about
3.30
Suppose we have a loaded die which gives the outcomes 1 through 6 according to the following probability distribution.Note that for this die all outcomes are not equally likely as they would be if this were a fair die. If this die is rolled 6000 times, the number of times we get a 2 or a 3 should be about
3000
Students at University X must be in one of the class ranks, Freshman, Sophomore, Junior, or Senior. At University X, 35% of the students are Freshmen and 30% are Sophomores. If a student is selected at random, the probability he or she is either a Junior or a Senior is
35%
A psychology instructor asked the 100 females in her class to rate their intelligence on a scale of 1 to 10. The ratings were What was the mean ranking for the females in this class?
6.66
A survey was conducted of students asking about their usage of marijuana in the last year (Never, Occasional, Regular) and the amount of alcohol and/or marijuana usage by their parents (Neither, One, Both). Here is a table of data.The conditional probability that the parents use one of alcohol or marijuana given a student never used marijuana is
68/226 = 0.30 = 30%
A fifth grade teacher gives homework every night in both mathematics and language arts. The time to complete the mathematics homework has a mean of 30 minutes and a standard deviation of 10 minutes. The time to complete the language arts assignment has a mean of 40 minutes and a standard deviation of 12 minutes. The time to complete the mathematics and the time to complete the language arts homework has a correlation ρ = -0.3. The mean time to complete the entire homework assignment
70 minutes
Which of the following events are disjoint
Choose a student at random from a statistics class. Event A is that the student is a Junior. Event B is that the student is a Senior.
A system has two components that operate in parallel, as shown in the diagram below. Since the components operate in parallel, at least one of the components must function properly if the system is to function properly. The probabilities of failure for components 1 and 2 during one period of operation are 0.20 and 0.03, respectively. Let F denote the event that component 1 fails during one period of operation and G denote the event that component 2 fails during one period of operation. The component failures are independent. The event corresponding to the above system functioning properly during one period of operation is
F^C or G^C
A standard deck of cards has 52 cards. The cards have one of two colors: 26 cards in the deck are red and 26 are black. The cards have one of four denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). Two cards are selected at random and the denomination is recorded. The event H is defined as the event that the first card is hearts. Which of the following correctly defines event H?
H = {(hearts, diamonds), (hearts, clubs), (hearts, spades), (hearts, hearts)}
Consider any two events A and B, such that P(A) ≠ 0 and P(B) ≠ 0. Which of the following statements is always FALSE?
If events A and B are independent, then P(A and B) = 0.
A penny is tossed. We observe whether it lands heads up or tails up. Suppose the penny is a fair coin; that is, the probability of heads is one-half and the probability of tails is one-half. What does this mean?
If the coin is tossed many, many times, the proportion of tosses that land heads will be approximately one-half, and this proportion will tend to get closer and closer to one-half as the number of tosses increases.
A college basketball player makes 80% of his free throws. At the beginning of a game he misses his first two free throws. We may correctly conclude
Neither answer is correct
On a certain airline, the chance the early flight from Atlanta to Chicago is full is 0.8. The chance the late flight is full is 0.7. The chance both flights are full is 0.6. Can we believe the two flights being full are independent events?
No
Which of the following is not a general rule for elementary probability for events A and B?
P(A) < 1 for any event A
A standard deck of cards has 52 cards. The cards have one of two colors: 26 cards in the deck are red and 26 are black. The cards have one of four denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). Two cards are selected at random and the color is recorded. Which of the following is the correct sample space S for the set of possible outcomes?
S = {(red, red), (red, black), (black, red), (black, black)}
Which of the following define a complete and valid probability model?
S = {H, T}; P(H) = 1/4, P(T) = 3/4
A coin is tossed, and then a six-sided die is rolled. Which of the following defines the sample space S?
S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
A phenomenon is observed many, many times under identical conditions. The proportion of times a particular event A occurs is recorded. What does this proportion represent?
The probability of the event A
Which of the following best describes what is meant by the probability of the outcome of a random phenomenon?
The proportion of times the outcome would occur in a very long series of repetitions
Which of the following are independent trials?
The results of a coin flip after rolling two dice and the first character of a license plate and the color of the car.
Suppose we have two independent random variables X and Y. Which of the following statements about X and Y is FALSE?
The variance of the difference of X - Y is the difference of their variances.
To win the Maryland Powerball® Lottery, you must select your own six numbers to play. Most people use numbers that are special to them, like anniversary dates or their children's birth dates. On the day of the lottery, the lottery officials randomly select five white balls, each with a number somewhere between 1 and 59, and one red Powerball® with a number somewhere between 1 and 35. You win a prize by matching some or all of the numbers drawn. Would winning the lottery be an example of a random phenomenon?
Yes, because the numbers drawn are random.
The amount of time it takes you to complete an exam in a statistics course is an example of a _______ random variable.
continuous
The number of hours of sleep you had last night is an example of a ______ random variable.
continuous
When two random variables are not independent, the variance between the two random variables depends on the _____.
correlation
Checkers is a board game played between two players, who alternate moves. The board is square, with sixty-four smaller squares, arranged in an eight-by-eight grid. The smaller squares are alternately light and dark colored, in the famous "checker-board" pattern. Each player starts with 12 pieces. You win by capturing all your opponent's pieces. This is accomplished by jumping over a piece, diagonally, to the adjacent vacant square beyond the piece. If each player's goal is to win the game, then each move is considered _________.
dependent
The probability distribution of random variable X is defined as follows. Table 0,.3 2,.1 ect
discrete
Suppose we toss a penny and a nickel. Let A be the event that the penny is a head and B be the event that the nickel is a tail. The events A and B are
independent
You are taking a basic statistics class. On the first exam you score poorly and receive only 10 out of 100 points. You decide to get a tutor for the next exam and study quite a bit more. You end up scoring much better and receive 80 out of 100 points. The scores on your first and second exam are considered _________.
independent
On a certain airline, the chance the early flight from Atlanta to Chicago is full is 0.8. The chance the late flight is full is 0.7. The chance both flights are full is 0.6. Are the two flights being full independent events?
no
A game consists of drawing three cards at random from a deck of playing cards. You win $3 for each red card that is drawn. It costs $2 to play. For one play of this game, the sample space s for the net amount you win (after deducting the cost of play) is
s = {-$2, $1, $4, $7}
A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. Imagine you stick your hand into the refrigerator and pull out a piece of fruit at random. What is the sample space for this process?
s = {apple, orange, banana, pear, peach, plum, mango}
