Probability Unit Test Review~ amdm

You are the manager of a retail store, and you have been tasked with finding the return rate on a certain brand of laptop computers. You have assembled the data on the number of computers sold and the number returned over the past six months in the table below. Using the table as experimental data, if your store has 379 laptops returned in April, how many laptops are likely to have been sold in April? a. 1,578 b. 1,740 c. 1,743 d. 2,219

C. 1,743

The partially filled contingency table gives the frequencies of the data on age (in years) and sex from the residents of a retirement home. What is the relative frequency for males in the age group 60-69? a. 1/2 c. 1/4 b. 13/40 d. 9/40

C. 1/4

A dog store has 3 female Chihuahuas. 14 of the 25 dogs at the store are not Chihuahuas. What is the probability that a dog selected at random is female, given it is a Chihuahua? A. 3/25 B. 3/14 C. 3/11 D. 11/25

C. 3/11

When two dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (2,1) (3,1) (4,1) (5,1) (6,1) (1,2) (2,2) (3,2) (4,2) (5,2) (6,2) (1,3) (2,3) (3,3) (4,3) (5,3) (6,3) (1,4) (2,4) (3,4) (4,4) (5,4) (6,4) (1,5) (2,5) (3,5) (4,5) (5,5) (6,5) (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) Let x be the sum of the two numbers. Let P be the probability of the desired outcome. Compare the following charts and determine which chart shows the probability distribution for the sum of the two numbers. a. Chart A b. Chart B c. Chart C d. None of them

B. Chart B

If a circle with a diameter of 57.75 m is inscribed in a square, what is the probability that a point picked at random in the square is in the shaded region? Round the answer to the nearest thousandth. A. 0.005 B. 0.027 C. 0.215 D. 0.785

C. 0.215

Consider a game in which you draw playing cards from a standard 52-card deck, one at a time. If a player draws a face card (a jack, a queen, or a king), the player is awarded 10 points. Any other card drawn costs the player 3 points. What is the expected value of drawing a card in this game? A. 0 points B. 3 points C. 6.5 points D. 10 points

A. 0

A computer is programmed to generate a sequence of three digits, where each digit is either 0 or 1, and each of these is equally likely to occur. Construct a sample space that shows all possible three-digit sequences of 0s and 1s and then find the probability that a sequence will contain at least one 0. a. 000, 001, 010, 011, 100, 101, 110, 111; P(at least one 0) = 7/8 b. 000, 001, 010, 100, 101, 110 ; P(at least one 0) = 6/6 c. 100, 101, 110, 111; P(at least one 0) = 3/4 d. 000, 001, 010, 011; P(at least one 0) = 4/8 = 1/2

A. 000, 001, 010, 011, 100, 101, 110, 111; P(at least one 0) = 7/8

Sharon is considering trying to open a new business within the next few years, and she is doing research to determine what kind of businesses tend to be successful. So far, she has compiled two tables. The first shows the number of businesses of several types started in Sharon's city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category. Using the tables as experimental data, determine whether it is more likely for a new retail establishment to succeed and earn profits of $50,000 or more, or whether it is more likely for a new service establishment to succeed and earn profits of $25,000 or less, and how much more likely the one situation is than the other. Express all probabilities as percentages to two decimal places, and express differences by number of percentage points (for example, 23% is 5 percentage points greater than 18%). a. The situation involving the retail establishment has a probability 0.99 percentage points higher than the situation involving the service establishment. b. The situation involving the retail establishment has a probability 4.91 percentage points higher than the situation involving the service establishment. c. The situation involving the service establishment has a probability 3.11 percentage points higher than the situation involving the retail establishment. d. The situation involving the service establishment has a probability 6.35 percentage points higher than the situation involving the retail establishment.

C. The situation involving the service establishment has a probability 3.11 percentage points higher than the situation involving the retail establishment.

Say that you put the set of tiles shown below into a bag and conduct a series of trials in which you draw one tile randomly from the bag, record the color, and replace it. The table below shows the number of times in each set of trials that you drew a blue tile. Between the theoretical probability that you will draw a blue tile and the experimental probability that you will draw a blue tile, which is greater, and how much greater is it? Express all probabilities as percentages to two decimal places, and express differences by number of percentage points (for example, 12% is 2 percentage points greater than 10%). a. The experimental probability is 6.67 percentage points greater than the theoretical probability. b. The experimental probability is 2.00 percentage points greater than the theoretical probability. c. The theoretical probability is 1.73 percentage points greater than the experimental probability. d. The theoretical probability is 0.77 percentage points greater than the experimental probability.

C. The theoretical probability is 1.73 percentage points greater than the experimental probability.

Jeremy randomly selected a round tile and a square tile from the sets shown below. What is the probability that Jeremy selected either two blue tiles or two white tiles? a. 23/36 b. 4/9 c. 7/72 d. 1/40

D. 1/40

What is the probability that a randomly thrown dart that lands within the rectangle lands within a shaded region? All of the circles are congruent, and the diameter of each circle is 100 cm. A. 39/200 B. 49/250 C. 98/125 D. 157/200

D. 157/200

How many different 4-digit sequences can be formed using the digits 0, 1,..., 6 if repetition of digits is allowed? a. 1296 c. 24 b. 20 d. 2401

D. 2401

What is the probability that a randomly thrown dart hits a blue or yellow region, given that it hits the square board? The radii of the circles are 2, 4, 6, 8, and 10 feet, respectively, and the square board has a side length of 21 feet. A. 8/324 B. 10/441 C. 21/324 D. 314/441

D. 314/441

A card is picked at random from a standard deck of cards. What is the sample space for this experiment if you were trying to find P(face card)? a. Sample space = 12 b. Sample space = 3/13 c. Sample space = 12/52 d. Sample space = 52

D. Sample space = 52

A basketball player is shooting free throws blindfolded. He shoots in groups of 4 shots. Assume that it is equally likely that he will hit or miss a shot. Design and do a simulation to determine the probability that he will hit at least 75% of his shots within the groups. (Hint: Use coins.)

Possible answer: a. Use 4 coins. Let heads = hit and tails = miss. Toss each coin and record the results in a table. Coin 1Coin 2Coin3Coin 4Set 1HHHHSet 2HTHHSet 3HHTHSet 4THTTSet 5 Repeat the coin tosses until you have recorded 50 sets of 4 tosses each. b. Count the successful outcomes—those with three or four heads. Coin 1Coin 2Coin3Coin 4SuccessSet 1HHHHxSet 2HTHHxSet 3HHTHxSet 4THTTSet 5 c. Write a ratio comparing successful outcomes with total outcomes.