Lesson 7.1
Lesson 7.2
Lesson 7.3
Lesson 8.1
Lesson 8.2
100
In probability and statistics, a random phenomenon is
(a) something that is completely unexpected or surprising
(b) something that has a limited set of outcomes, but when each outcome occurs is completely unpredictable.
(c) something that appears unpredictable, but each individual outcome can be accurately predicted with appropriate mathematical or computer modeling.
(d) something that is unpredictable from one occurrence to the next, but over the course of many occurrences follows a predictable pattern.
(d)
100
A friend rolls cheap dice many times. He reports that the probabilities of the possible outcomes are about as follows. Is this a legitimate probability model?
(a) Yes.
(b) No -- the faces must all have the same probability.
(c) No -- the 3 and 4 faces are opposite each other, so they must have the same probability.
(d) No -- the total probability for all faces is wrong.
(a)
100
A household is a group of people living together at the same address. Choose one American household at random and record how many people it contains. Here are the probabilities. What is the probability that the household chosen contains only one person?
(a) 0.15
(b) 0.25
(c) 0.35
(d) 0.75
(b)
100
An exam has 40 multiple-choice questions, each with 5 choices. Only 1 of the 5 choices for each question is correct. If you used a table of random digits to randomly choose your answer on all questions, about how many answers would you expect to get correct?
(a) 40
(b) 0
(c) 20
(d) 8
(d)
100
“A ten-sided die has ten possible outcomes. Therefore, rolling a ten-sided die twice has 100 possible outcomes.” This statement is supported by
(a) the permutation counting principle.
(b) the combination counting principle.
(c) the factorial counting principle.
(d) the multiplication counting principle.
(d)
200
If I toss a fair coin five times and the outcomes are TTTTT, then the probability that tails appears on the next toss is
(a) 0.5
(b) less than 0.5
(c) greater than 0.5
(d) 0
(a)
200
Dice have six faces, showing 1 to 6 pips (spots). If a die is balanced, all six faces are equally likely. What must be the probability of each face?
(a) 1/10, or 0.10.
(b) 1/6, or 0.167.
(c) 2/10, or 0.20.
(d) 2/6, or 0.333.
(b)
200
If P(A) = 0.5 and P(B) = 0.3, what must P(B|A) be if events A and B are independent?
(a) 0.15
(b) 0.3
(c) 0.6
(d) 0.8
(b)
200
In government data, a family consists of two or more persons who live together and are related by blood or marriage. Choose an American family at random and count the number of people it contains. Here is the assignment of probabilities for your outcome. What is the probability that the family you choose has more than 2 people?
(a) 0.35
(b) 0.42
(c) 0.58
(d) 1.00
(c)
200
You have eight acts signed up to perform in the school’s talent show. How many different ways can you order the acts in the program?
(a) 8
(b) 64
(c) 256
(d) 40,320
(d)
300
Two events are independent if
(a) If one occurs, the probability that the other occurs is 1.
(b) If one occurs, the probability that the other occurs is 0.
(c) The probability that one occurs is the complement of the probability that the other occurs.
(d) The probability that one occurs is not influenced by whether the other has occurred.
(d)
300
If a coin has 0.6 probability coming up tails, the probability that it comes up heads is
(a) 0.5
(b) -0.2
(c) 0.4
(d) 0.6
(c)
300
The Venn diagram below describes the proportion of students who take chemistry and Spanish. Suppose one student is chosen at random. Find the value of P(A U B) and describe it in words.
(a) 0.1; The probability that the student takes both Chemistry and Spanish.
(b) 0.1; The probability that the student takes either Chemistry or Spanish, but not both.
(c) 0.5; The probability that the student takes either Chemistry or Spanish, but not both.
(d) 0.6; The probability that the student takes either Chemistry or Spanish, or both.
(d)
300
A sampling distribution is
(a) The distribution of values of a random variable for all individuals in a sample.
(b) A probability distribution describing any random phenomenon, such as flipping a coin or rolling two dice.
(c) A probability distribution listing all the possible values of a sample statistic and their probabilities.
(d) A probability distribution listing all the possible values of a population parameter and their probabilities.
(c)
300
You and 10 of your friends want to go see a movie. You have a car and room for 4 more people. How many different groups of people can go to the movie in your car?
(a) 4
(b) 16
(c) 210
(d) 252
(c)
400
The probability that a randomly-selected person is left-handed is about 1/10. Which of the following statements must be true?
(a) If you randomly selected ten people, exactly one will be left-handed.
(b) In any randomly-selected group of 10000 people, exactly 1000 of them will be left-handed.
(c) As you randomly choose more and more people, the proportion of left-handers may start out quite far from 1/10, but it will get close to 1/10 as the number of people you select increases.
(d) (b) and (c) are true, but not (a).
(c)
400
In backgammon, one rolls a pair of two fair dice. The probability of getting a sum of 7 is
(a) 3/36
(b) 4/36
(c) 5/36
(d) 6/36
(d)
400
The following table compares the hand dominance of 200 Canadian high school students and what methods they prefer using to communicate with their friends. Suppose one student is chosen randomly from this group of 200. What is the probability that the student chosen is left-handed or prefers to communicate with friends in person?
(a) 0.065
(b) 0.17
(c) 0.425
(d) 0.53
(d)
400
A gambler who keeps placing $1 bets on roulette will, after a very large number of bets, find that his average winnings per bet are close to $0.947. (The house keeps the other $0.053 per bet.) The statistical term for the number $0.947 is
(a) the probability of winning a bet.
(b) the bias of a bet.
(c) a random number.
(d) the expected value of a bet.
400
5! =
(d)
500
You are playing a board game with some friends that involves rolling two six-sided dice. For eight consecutive rolls, the sum on the dice is 6. Which of the following statements is true?
(a) Each time you roll another 6, the probability of getting yet another 6 on the next roll goes down.
(b) Each time you roll another 6, the probability of getting yet another 6 on the next roll goes up.
(c) You should find another set of dice: eight consecutive 6’s is impossible with fair dice.
(d) The probability of rolling a 6 on the ninth roll is the same as it was on the first roll.
(d)
500
The card game Euchre uses a deck with 32 cards: Ace, King, Queen, Jack, 10, 9, 8, 7 of each suit. Suppose you choose one card at random from a well-shuffled Euchre deck. What is the probability that the card is an Ace?
(a) 1/32
(b) 1/13
(c) 1/8
(d) 1/2
(c)
500
One hundred high school students were asked if they had a dog, a cat, or both at home. Here are the results. If a single student is selected at random and you know she has a dog, what is the probability she also has a cat?
(a) 0.04
(b) 0.12
(c) 0.22
(d) 0.75
(d)
500
The law of large numbers says:
(a) Large numbers are subject to more variability than small numbers, and are therefore harder to estimate with confidence.
(b) If one simulates a random phenomenon many times, the variability in the estimate of the expected value increases as the number of simulations increases.
(c) The larger the magnitude of an expected value, the more simulations are required to estimate it.
(d) If a random phenomenon with numerical outcomes is repeated many times, the mean of the observed outcomes approaches the expected value.
(d)
500
How many four-digit numbers do not end in 7, 8, or 9?
(a) 840
(b) 2,401
(c) 5,400
(d) 6,300
(d)