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mathematics
precalculus

Questions and Answers of Precalculus

If P(B) = 0.30, P(A ∪ B) = 0.65, and P(A ∩ B) = 0.15, find P(B).
If P(A) = 0.60, P(A ∪ B) = 0.85, and P(A ∩ B) = 0.05, find P(B).
Find the probability of the indicated event if P(A) = 0.25 and P(B) 0.45.P(A ∩ B) if A, B are mutually exclusive
Find the probability of the indicated event if P(A) = 0.25 and P(B) 0.45.P( A ∪ B) if A, B are mutually exclusive
Find the probability of the indicated event if P(A) = 0.25 and P(B) 0.45.P(A ∩ B) if P(A ∪ B) = 0.6
Find the probability of the indicated event if P(A) = 0.25 and P(B) 0.45.P(A ∪ B) if P(A ∩ B) = 0.15
Two fair dice are rolled. Determine the probability that the sum of the two dice is 12.
Two fair dice are rolled. Determine the probability that the sum of the two dice is 3.
Two fair dice are rolled. Determine the probability that the sum of the two dice is 11.
Two fair dice are rolled. Determine the probability that the sum of the two dice is 7.
Assume equally likely outcomes.Determine the probability of having 2 girls and 2 boys in a 4-child family.
Assume equally likely outcomes.Determine the probability of having 1 girl and 3 boys in a 4-child family.
Assume equally likely outcomes.Determine the probability of having 3 girls in a 3-child family.
Assume equally likely outcomes.Determine the probability of having 3 boys in a 3-child family.
An urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles.If one marble is selected, determine the probability that it is black.
An urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles.If one marble is selected, determine the probability that it is white.
The sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose that the outcomes are equally likely.Compute the probability of the event F: “an odd number.”
The sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose that the outcomes are equally likely.Compute the probability of the event E: “an even number.”
The sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose that the outcomes are equally likely.Compute the probability of the event F = {3. 5. 9. 10}
The sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose that the outcomes are equally likely.Compute the probability of the event E = {1, 2, 3}
A die is weighted so that a six cannot appear. The other faces occur with the same probability. What probability should we assign to each face?
A die is weighted so that an odd-numbered face is twice as likely to occur as an even-numbered face. What probability should we assign to each face?
A coin is weighted so that tails is twice as likely as heads to occur.What probability should we assign to heads? to tails?
A coin is weighted so that heads is four times as likely as tails to occur.What probability should we assign to heads? to tails?
Consider the experiment of tossing a coin twice. The table lists six possible assignments of probabilities for this experiment. Using this table, answer the following questions. Which of the
Consider the experiment of tossing a coin twice. The table lists six possible assignments of probabilities for this experiment. Using this table, answer the following questions. Which of the
Consider the experiment of tossing a coin twice. The table lists six possible assignments of probabilities for this experiment. Using this table, answer the following questions. Which of the
Consider the experiment of tossing a coin twice. The table lists six possible assignments of probabilities for this experiment. Using this table, answer the following questions. Which of the
Use the following spinners to construct a probability model for each experiment.Spin spinner III, then spinner I twice. What is the probability of getting Forward, followed by a 1 or a 3, followed by
Use the following spinners to construct a probability model for each experiment. Spin spinner I twice, then spinner II. What is the probability of getting a 2, followed by a 2 or a 4, followed
Use the following spinners to construct a probability model for each experiment. Spin spinner II, then I, then III. What is the probability of getting Yellow, followed by a 2 or a 4, followed by
Use the following spinners to construct a probability model for each experiment. Spin spinner I, then II, then III. What is the probability of getting a 1, followed by Red or Green, followed by
Use the following spinners to construct a probability model for each experiment. Spin spinner III, then spinner II. What is the probability of getting Forward, followed by Yellow or Green?
Use the following spinners to construct a probability model for each experiment. Spin spinner I, then spinner II. What is the probability of getting a 2 or a 4, followed by Red? Yellow Forward
Construct a probability model for the experiment. Tossing one fair coin three times
Construct a probability model for the experiment. Tossing three fair coins once
Construct a probability model for the experiment. Tossing a fair coin, a fair die, and then a fair coin
Construct a probability model for the experiment. Tossing two fair coins, then a fair die
Construct a probability model for the experiment. Tossing two fair coins once
Construct a probability model for the experiment. Tossing a fair coin twice
Determine whether the following is a probability model. Probability Outcome Erica 0.3 0.2 Joanne 0.1 Laura Donna 0.5 Angela -0.1
Determine whether the following is a probability model. Probability Outcome Linda 0.3 Jean 0.2 Grant 0.1 0.3 Jim
Determine whether the following is a probability model. Probability Outcome 0.4 Steve Bob 0.3 Faye 0.1 0.2 Patricia
Determine whether the following is a probability model. Probability Outcome 0.2 2 0.3 3 0.1 4 0.4
In a probability model, which of the following numbers could be the probability of an outcome? 3 1.5 2 4 3 4
In a probability model, which of the following numbers could be the probability of an outcome? 0 0.01 0.35 -0.4 1 1.4
True or False.In a probability model, the sum of all probabilities is 1.
True or False.The probability of an event can never equal 0.
The______of an event E is the set of all outcomes in the sample space S that are not outcomes in the event E.
When the same probability is assigned to each outcome of a sample space, the experiment is said to have______outcomes.
How many arrangements of answers are possible in a multiple-choice test with 5 questions, each of which has 4 possible answers?
Explain the difference between a permutation and a combination. Give an example to illustrate your explanation.
A combination lock displays 50 numbers. To open it, you turn to a number, then rotate clockwise to a second number, and then counterclockwise to the third number. (a) How many different lock
On a basketball team of 12 players, 2 only play center, 3 only play guard, and the rest play forward (5 players on a team: 2 forwards, 2 guards, and 1 center). How many different teams are possible,
A basketball team has 6 players who play guard (2 of 5 starting positions). How many different teams are possible, assuming that the remaining 3 positions are filled and it is not possible to
In the World Series the American League team and the National League team play until one team wins four games. If the sequence of winners is designated by letters (for example, NAAAA means that the
A baseball team has 15 members. Four of the players are pitchers, and the remaining 11 members can play any position. How many different teams of 9 players can be formed?
In the National Baseball League, the pitcher usually bats ninth. If this is the case, how many batting orders is it possible for a manager to use?
In the American Baseball League, a designated hitter may be used. How many batting orders is it possible for a manager to use? (There are 9 regular players on a team.)
A defensive football squad consists of 25 players. Of these, 10 are linemen, 10 are linebackers, and 5 are safeties. How many different teams of 5 linemen, 3 linebackers, and 3 safeties can be
The U.S. Senate has 100 members. Suppose that it is desired to place each senator on exactly 1 of 7 possible committees. The first committee has 22 members, the second has 13, the third has 10, the
An urn contains 15 red balls and 10 white balls. Five balls are selected. In how many ways can the 5 balls be drawn from the total of 25 balls: (a) If all 5 balls are red? (b) If 3 balls
An urn contains 7 white balls and 3 red balls. Three balls are selected. In how many ways can the 3 balls be drawn from the total of 10 balls: (a) If 2 balls are white and 1 is red? (b) If
How many different 11-letter words (real or imaginary) can be formed from the letters in the word MATHEMATICS?
How many different 9-letter words (real or imaginary) can be formed from the letters in the word ECONOMICS?
The student relations committee of a college consists of 2 administrators, 3 faculty members, and 5 students. Four administrators, 8 faculty members, and 20 students are eligible to serve. How many
A student dance committee is to be formed consisting of 2 boys and 3 girls. If the membership is to be chosen from 4 boys and 8 girls, how many different committees are possible?
In how many ways can 5 people each have different birthdays? Assume that there are 365 days in a year.
In how many ways can 2 people each have different birthdays? Assume that there are 365 days in a year.
How many different license plate numbers can be made using 2 letters followed by 4 digits selected from the digits 0 through 9, if (a) letters and digits may be repeated? (b) letters may be
Five different mathematics books are to be arranged on a student’s desk. How many arrangements are possible? Sullivan Sullivan Finite Mathematics Sullivan Pearson Sullivan Pearson Pearson
How many arrangements of answers are possible for a true/false test with 10 questions?
In how many ways can a committee of 3 professors be formed from a department having 8 professors?
In how many ways can a committee of 4 students be formed from a pool of 7 students?
Companies whose stocks are listed on the New York Stock Exchange (NYSE) have their company name represented by either 1, 2, or 3 letters (repetition of letters is allowed). What is the maximum number
How many different four-letter codes are there if only the letters A, B, C, D, E, and F can be used and no letter can be used more than once?
How many different three-letter codes are there if only the letters A, B, C, D, and E can be used and no letter can be used more than once?
In how many ways can 5 different boxes be stacked?
In how many ways can 4 people be lined up?
How many three-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9? Repeated digits are allowed.
How many three-digit numbers can be formed using the digits 0 and 1? Repeated digits are allowed.
How many two-letter codes can be formed using the letters A, B, C, D, and E? Repeated letters are allowed.
How many two-letter codes can be formed using the letters A, B, C, and D? Repeated letters are allowed.
. List all the combinations of 6 objects 1, 2, 3, 4, 5, and 6 taken 3 at a time. What is C(6, 3)?
List all the combinations of 4 objects 1, 2, 3, and 4 taken 3 at a time. What is C(4, 3)?
List all the combinations of 5 objects a, b, c, d, and e taken 2 at a time. What is
List all the combinations of 5 objects a, b, c, d, and e taken 3 at a time. What is C(5, 3)?
List all the ordered arrangements of 6 objects 1, 2, 3, 4, 5, and 6 choosing 3 at a time without repetition. What is P(6,3)?
List all the ordered arrangements of 4 objects 1, 2, 3, and 4 choosing 3 at a time without repetition. What is P(4, 3)?
List all the ordered arrangements of 5 objects a, b, c, d, and e choosing 2 at a time without repetition. What is P(5, 2)?
List all the ordered arrangements of 5 objects a, b, c, d, and e choosing 3 at a time without repetition. What is P(5, 3)?
Use formula (2) to find the value of each combination.C(18, 9)
Use formula (2) to find the value of each combination.C(26, 13)
Use formula (2) to find the value of each combination.C(18, 1)
Use formula (2) to find the value of each combination.C(15, 15)
Use formula (2) to find the value of each combination.C(6, 2)
Use formula (2) to find the value of each combination.C(7, 4)
Use formula (2) to find the value of each combination.C(8, 6)
Use formula (2) to find the value of each combination.C(8, 2)
Find the value of the permutation. P(8, 3)

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