Unit Test 9
What is the probability of getting tails each time if a coin is tossed 4 times?
1/16
A box contains 6 nuts, 8 bolts, and 4 screws. If 3 objects are selected in succession randomly, what is the probability of selecting a nut, then a bolt, then a screw, if replacement occurs each time?
8/243
A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women?
A.
An investor would like to invest $60,000 in 2 stocks from a list of 6 suggested by a broker. How many investments of $30,000 each are possible?
A. 15
How many ways can a president, vice president, and secretary be selected from a class of 30 students?
D. 24,360
A certain website requires that passwords be 4 letters in a row, followed by an integer. How many passwords can be made by following these rules? The password is not case-sensitive.
D. 4,569,760
Evaluate. 3P2
D. 6
A movie rental store has a movie selection that consists of 4 action movies, 3 horror movies, 2 drama movies, and 3 comedies. If you select two movies at random, what is the probability that you select 2 action movies?
D. 1/11
Find the probability of drawing a red ace, then a red king from a standard deck of cards without replacement.
D. 1/663, or about 0.0015
Which of the following expressions represents 12P5
D. 12!/7!
A fruit basket contains 6 apples and 8 oranges. Sarah randomly selects one, puts it back, and then randomly selects another. What is the probability that both selections were oranges?
D. 16/49
If an event can never happen, its probability is a negative number.
False
If an event can succeed in s ways and fail in f ways, then the odds against the event is s:f.
False
Find the odds of an event if the probability of the event is given to be: 1/13
a. 1:12
Javier's movie collection consists of 3 action movies, 5 comedies, and 9 dramas. In a rush, he randomly grabs 3 movies to bring on a plane flight. What is the probability that he chose 2 action movies and 1 comedy?
A.
Which of the following statements is true for permutations?
A. The order of objects counted in a permutation always matters.
Given the following circumstances, what counting formula should be used? 1) The order of selection is important. 2) Repetition is not allowed. 3) There are no identical objects.
A. nPr
Two pens are selected at random from a pen stand containing three blue and two black pens. The table and the relative-frequency histogram show the distribution of the number of blue pens chosen. Find the probability. P(0 blue pens)
A. 1/10
Two pens are selected at random from a pen stand containing three blue and two black pens. The table and the relative-frequency histogram show the distribution of the number of blue pens chosen. Find the probability. P(0 blue pens)
A. 1/10
Two pens are selected at random from a pen stand containing three blue and two black pens. The table and the relative-frequency histogram show the distribution of the number of blue pens chosen. Find the probability. P(2 black pens)
A. 1/10
What is the probability of getting a 4 each time if a die is rolled 3 times?
A. 1/216
Suppose you select 2 letters at random from the word compute. Find each probability. P(2 vowels)
A. 1/7
Three tickets are selected at random from a box of tickets bearing numbers from 1 to 30. The table and the relative-frequency histogram show the distribution of the number of even-numbered tickets chosen. Find the given probability. P(3 even-numbered tickets)
A. 13/116
Suppose you roll two number cubes. The graph below represents the probability distribution for the sample space {sum of numbers is less than 6, sum of numbers is greater than 6, sum of numbers equals 6}. Which answer represents the given probability? P(sum of numbers is greater than 6)
A. 21/36
8 men and 6 women arrive separately in a random fashion to a meeting. What is the probability that the first 4 people to show up are men?
B.
A game is played where 26 tiles are in a bag. Each tile has a different letter of the alphabet on it. If you draw 5 letters, what is the probability of the letters being M-U-S-I-C in order, if there is no replacement?
B.
Determine the number of ways to choose a set of 9 pencils from a selection of 10.
B. 10
In how many ways can a group of 4 people be selected for a party planning committee from a class of 25?
B. 12,650
From a group of 10 people, 5 are selected at random to participate in a game show. In how many ways can the 5 people be selected?
B. 252
If 8 people meet, and each person shakes hands with all of the other people exactly once, how many handshakes occurred?
B. 28
From a group of 5 freshmen, 3 sophomores, 4 juniors, and 3 seniors, how many 5-person committees are possible?
B. 3,003
How many outfits are possible from 4 pairs of jeans, 6 shirts, and 2 pairs of shoes? Assume that the outfit consists of 1 pair of jeans, 1 shirt, and 1 pair of shoes.
B. 48
A student is attempting to solve a math problem, shown below. Which statement best applies to the student's sample mathematical work? Given 4C2, I first apply the formula for combinations, which gives --- Evaluating this, I get a final answer of 1.
B. The simplification step is incorrect
Laura has moved to a new apartment. Her schoolbooks comprising of different subjects are mixed in a bag during the move. Four books are of mathematics, three are English, and six are science. If Laura opens the bag and selects books at random, find the given probability. P(3 English books)
B. 1/286
There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected for a stage performance. Find the probability of the following selection. P(2 brown-haired children)
B. 10/23
Suppose you select 2 letters at random from the word compute. Find each probability. P(2 consonants)
B. 2/7
Find the odds of an event if the probability of the event is given to be: 2/5
B. 2:3
A jar contains 6 chocolate chip cookies and 9 peanut butter cookies. Richard grabs 3 cookies at random to pack in his lunch. What is the probability that he drew 3 chocolate chip cookies?
B. 4/91
A jar contains 3 chocolate cookies, 5 peanut butter cookies, and 6 coconut cookies. If 3 cookies are selected in succession, what is the probability of selecting chocolate, then peanut butter, and then coconut cookies, if replacement occurs each time?
B. 45/1372
Which of the following values is the greatest?
B. 6P6
Ashley takes her 3-year-old brother Alex into an antique shop. There are 5 statues, 4 picture frames, and 3 vases on a shelf. Alex accidentally knocks 2 items off the shelf and breaks them. Choose the probability best described by 5/44
B. P(breaking a statue, then a statue)
Identify the expression below that represents mPn.
C.
Which of the following expressions represents 24C12
C.
If there are 4 Democrats and 3 Republicans on a committee, what is the probability that a Democrat will be the chair of the committee and a Republican will be the alternate? Assume that the chair and the alternate are chosen randomly. Round the answer to the nearest hundredth.
C. 0.29
A personal identification code consists of five digits (0 through 9). How many codes are possible?
C. 100,000
Evaluate. 6C4
C. 15
How many different groups of 3 movies can a person rent if there are 12 movies to choose from?
C. 220
A one-stog at Boise, Omaha, or Chicago. The flight then connects to either La Guardia or JFK airport, both in NYC. How many different routes are possible?
C. 6
A series of specialty license plates consists of three digits followed by two letters. How many unique license plates are possible?
C. 676,000
In how many ways can 6 people be arranged in a line?
C. 720
How many different batting orders are possible if 9 people are chosen from a group of 12 on a baseball team?
C. 79,833,600
What is the probability of drawing a spade each time a card is drawn from a deck of 52 cards 3 times, if replacement occurs each time?
C. 1/64
Laura has moved to a new apartment. Her schoolbooks comprising of different subjects are mixed in a bag during the move. Four books are of mathematics, three are English, and six are science. If Laura opens the bag and selects books at random, find the given probability. P(1 science and 2 mathematics books)
C. 18/143
Find the odds of an event if the probability of the event is given to be : 2/3
C. 2:1
There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected for a stage performance. Find the probability that a black-haired student and a brown-haired student are selected for a stage performance.
C. 32/69
Ashley takes her 3-year-old brother Alex into an antique shop. There are 5 statues, 4 picture frames, and 3 vases on a shelf. Alex accidentally knocks 2 items off the shelf and breaks them. Choose the probability best described by: 1/22
C. P (breaking 2 vases)
Which of the following expressions represents 50P10
D. 50!/40!
Determine whether the given event is independent or dependent. Then find the probability. There are 3 literature books, 4 geography books, and 3 science books on a shelf. If 3 books are chosen at random one after the other, what is the probability that a literature book, a geography book, and a science book are selected if replacement does not take place?
a. dependent; 1/20
Determine whether the given event is independent or dependent. Then find the probability. There are 3 strawberry ice creams, 4 chocolate ice creams, and 7 vanilla ice creams on a tray. Barbara selects 2 ice creams at random without replacement. What is the probability that she selects 2 chocolate ice creams?
a. dependent; 6/91
Determine whether the given event is independent or dependent. Then find the probability. In a game show, cards are displayed showing different prizes. There are 10 cards showing a car, 10 cards showing a holiday trip, and 20 cards showing a house. If the host selects 6 cards in succession without replacement, what is the probability of getting 3 cards showing a car, followed by 2 cards showing a holiday trip, and finally, 1 card showing a house?
b. dependent; 30/63973
Find the odds of an event if the probability of the event is given to be: 3/8
d. 3:5
Determine whether the given event is independent or dependent. Then find the probability. A bowl contains 3 red, 8 blue, and 7 black beads. Margaret randomly selects 3 beads one after the other without replacement. Find the probability of getting a red, blue, and black bead, in that order.
d. dependent; 7/204
