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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

If the probability is .51 that a candidate wins the election, what is the probability that he loses?
The payoff table for two courses of action, A1 or A2, is given below. Which of the two actions will produce the largest expected value? What is it? Pi .1 .2 .4 .3 A₁ xi -
A small combination lock has 3 wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is a particular sequence of 3 digits with no repeats, what is the probability of a person
Five dice are rolled all at once. On each of the first four dice, the outcome is a 6. What is the probability that a 6 shows on the 5th dice?
An experiment consists of rolling a pair of fair dice. Let X be the random variable associated with the sum of the values that turn up. (A) Find the probability distribution for X. (B) Find the
In Problems 35 and 36, an urn contains 4 red and 5 white balls. Two balls are drawn in succession without replacement. If the second ball is white, what is the probability that the first ball was
In Problems 35 and 36, an urn contains 4 red and 5 white balls. Two balls are drawn in succession without replacement. If the second ball is red, what is the probability that the first ball was red?
A game has an expected value to you of $100. It costs $100 to play, but if you win, you receive $100,000 (including your $100 bet) for a net gain of $99,900. What is the probability of winning? Would
In Problems 37 and 38, urn 1 contains 7 red and 3 white balls. Urn 2 contains 4 red and 5 white balls. A ball is drawn from urn 1 and placed in urn 2. Then a ball is drawn from urn 2.If the ball
Twenty thousand students are enrolled at a state university. A student is selected at random, and his or her birthday (month and day, not year) is recorded. Describe an appropriate sample space for
Compute the probability of event E if the odds in favor of E are (A) 3 8 (B) 7 (C) 4 1 (D) 49 51
A card is drawn at random from a standard 52-card deck. If E is the event “The drawn card is red” and F is the event “The drawn card is an ace,” then.(A) Find P(FE). (B) Test E and F for
In Problems 41 and 42, two balls are drawn in succession from an urn containing m blue balls and n white balls (m ≥ 2 and n ≥ 2). Discuss the validity of each statement. If the statement is
In Problems 41–45, urn U1 contains 2 white balls and 3 red balls; urn U2 contains 2 white balls and 1 red ball.Two balls are drawn out of urn U1 in succession. What is the probability of drawing a
A box of 10 flashbulbs contains 3 defective bulbs. A random sample of 2 is selected and tested. Let X be the random variable associated with the number of defective bulbs in the sample.(A) Find the
Compute the probability of event E if the odds in favor of E are 519 (A) 2 (B) 4 3 (C) 3 7 (D) 23 77
In Problems 41 and 42, two balls are drawn in succession from an urn containing m blue balls and n white balls (m ≥ 2 and n ≥ 2). Discuss the validity of each statement. If the statement is
In Problems 43–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If the odds for E equal the odds against E', then P(E) =
If 2 cards are drawn in succession from a standard 52-card deck without replacement and the second card is a heart, what is the probability that the first card is a heart?
In Problems 43–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If the odds for E are a: b, then the odds against E are b: a.
In Problems 43–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If P(E) + P(F) = P(EUF) + P(EF), then E and F are mutually
In Problems 45–50, a 3-card hand is dealt from a standard 52-card deck, and then one of the 3 cards is chosen at random. If only one of the cards in the hand is a club, what is the probability
In Problems 45–50, a 3-card hand is dealt from a standard 52-card deck, and then one of the 3 cards is chosen at random. If only two of the cards in the hand are clubs, what is the probability
From a standard deck of 52 cards, what is the probability of obtaining a 5-card hand (A) Of all diamonds? (B) Of 3 diamonds and 2 spades?Write answers in terms of nCr or nPr; do not evaluate.
Compute the indicated probabilities in Problems 47 and 48 by referring to the following probability tree: (A) P(M ∩ S).(B) P(R) .3 .7 M N- .4 .6 .2 .8 R S R S
In Problems 45–50, a 3-card hand is dealt from a standard 52-card deck, and then one of the 3 cards is chosen at random.If the chosen card is a club, what is the probability that it is the only
In a class of 20 students, two are twins. If 4 students are selected at random, what is the probability that the twins are selected?
Compute the indicated probabilities in Problems 47 and 48 by referring to the following probability tree: (A) P(N ∩ R) (B) P(S) .3 .7 M N- .4 .6 .2 .8 R S R S
In Problems 43–48, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If E and F are complementary events, then E and F are mutually
The command in Figure A was used on a graphing calculator to simulate 50 repetitions of rolling a pair of dice and recording the minimum of the two numbers. A statistical plot of the results is shown
In Problems 45–50, a 3-card hand is dealt from a standard 52-card deck, and then one of the 3 cards is chosen at random.If the chosen card is a club, what is the probability that all of the cards
In Problems 51–56, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If P(E) 1, then the odds for E are 1 : 1.
In Problems 45–50, a 3-card hand is dealt from a standard 52-card deck, and then one of the 3 cards is chosen at random.If the chosen card is not a club, what is the probability that none of the
If U1 and U2 are two mutually exclusive events whose union is the equally likely sample space S and if E is an arbitrary event in S such that P(E) ≠ 0, show that P(U| E) = n(USE) n(USE) + n(UշՈE)
In Problems 49–52, compute the odds in favor of obtaining At least 1 head when a single coin is tossed 3 times.
In Problems 51–56, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If E= F', then P(EUF) = P(E) + P(F).
In Problems 51–56, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If E and F are complementary events, then E and F are
In Problems 51–56, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If P(E ∪ F) = 1, then E and F are complementary events.
In Problems 51–56, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If E and F are independent events, then P(E)P(F) = P(ENF).
A card is drawn at random from a standard 52-card deck. Events M and N are M = the drawn card is a diamond. N - the drawn card is even (face cards are not valued). (A) Find P(NM). (B) Test M and N
In Problems 51–56, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If E and F are mutually exclusive events, then P(E) + P(F) =
An experiment consists of tossing three fair (not weighted) coins, except that one of the three coins has a head on both sides. Compute the probability of obtaining the indicated results in Problems
An experiment consists of tossing three fair (not weighted) coins, except that one of the three coins has a head on both sides. Compute the probability of obtaining the indicated results in Problems
You bet a friend $1 that you will get 1 or more double 6’s on 24 rolls of a pair of fair dice. What is your expected value for this game? What is your friend’s expected value? Is the game fair?
In a random sample of 1,000 people, it is found that 7% have a liver ailment. Of those who have a liver ailment, 40% are heavy drinkers, 50% are moderate drinkers, and 10% are nondrinkers. Of those
An experiment consists of tossing three fair (not weighted) coins, except that one of the three coins has a head on both sides. Compute the probability of obtaining the indicated results in Problems
An experiment consists of tossing three fair (not weighted) coins, except that one of the three coins has a head on both sides. Compute the probability of obtaining the indicated results in Problems
Two cards are drawn in succession without replacement from a standard 52-card deck. In Problems 60 and 61, compute the indicated probabilities. The second card is a heart given that the first card
In Problems 61–64, a single card is drawn from a standard 52-card deck. Calculate the probability of and odds for each event.A face card or a club is drawn.
An experiment consists of tossing three fair (not weighted) coins, except that one of the three coins has a head on both sides. Compute the probability of obtaining the indicated results in Problems
The first card is a heart given that the second card is a heart.
An experiment consists of tossing three fair (not weighted) coins, except that one of the three coins has a head on both sides. Compute the probability of obtaining the indicated results in Problems
In Problems 61–64, a single card is drawn from a standard 52-card deck. Calculate the probability of and odds for each event.A black card or an ace is drawn.
In Problems 63–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If P(A|B) = P(B), then A and B are independent.
In Problems 63–68, a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain.A single card is drawn from a standard deck. We are interested in whether or
In Problems 63–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If A and B are independent, then P(A|B) = P(B|A).
In Problems 63–68, a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain.A single fair coin is tossed. We are interested in whether the coin falls
Suppose that 3 white balls and 1 black ball are placed in a box. Balls are drawn in succession without replacement until a black ball is drawn, and then the game is over. You win if the black ball is
In Problems 63–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If A is nonempty and A ⊂ B, then P(A|B) P(A).
In Problems 63–68, a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain.A single fair die is rolled. We are interested in whether or not the number
If each of 4 people is asked to answer a multiple choice question having 7 different options, what is the probability that at most 3 of them select the same option?
In Problems 63–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If A and B are events, then P(A|B) ≤ P(B).
In Problems 63–68, a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain.A nickel and dime are tossed. We are interested in the number of heads that
Let A and B be events with nonzero probabilities in a sample space S. Under what conditions is P(A|B) equal to P(B|A)?
What is the probability that a number selected at random from the first 1,000 positive integers is (exactly) divisible by 6 or 8?
In Problems 63–68, a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain.A wheel of fortune has seven sectors of equal area colored red, orange,
In Problems 63–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If A and B are mutually exclusive, then A and B are
In Problems 63–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If two balls are drawn in succession, with replacement, from
In Problems 63–68, a sample space S is described. Would it be reasonable to make the equally likely assumption? Explain.A wheel of fortune has seven sectors of equal area colored red, orange,
In Problems 63–70, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. P(W₂R₂) = P(R₁ W₂)
(A) Is it possible to get 19 heads in 20 flips of a fair coin? Explain. (B) If you flipped a coin 40 times and got 37 heads, would you suspect that the coin was unfair? Why or why not? If you
An experiment consists of rolling two fair (not weighted) dice and adding the dots on the two sides facing up. Each die has the number 1 on two opposite faces, the number 2 on two opposite faces, and
An experiment consists of rolling two fair (not weighted) dice and adding the dots on the two sides facing up. Each die has the number 1 on two opposite faces, the number 2 on two opposite faces, and
For the experiment in Problem 71, what is the probability that no white balls are drawn? Data in Problem 71A box contains 2 red, 3 white, and 4 green balls. Two balls are drawn out of the box in
Thirteen boxes of drugs, including 3 that have expired, are sent to a chemist. The chemist will select three boxes at random and will return the entire shipment if 1 or more of the sample have
Show that if A and B are independent events with nonzero probabilities in a sample space S, then P(A|B) = P(A) and P(BA) = P(B)
In a group of n people (n ≤ 12), what is the probability that at least 2 of them have the same birth month? (Assume that any birth month is as likely as any other.)
Show that if A and B are events with nonzero probabilities in a sample space S, and either P(A|B) = P(A) or P(B|A) = P(B), then events A and B are independent.
Ten men in 80 and 4 women in 80 are left-handed. A person is selected at random and is found to be lefthanded. What is the probability that this person is a woman? (Assume that the ratio of men to
Show that P(A|A) 1 when P(A) ≠ 0.
Show that P(A|B) + P(A'|B) = 1.
Show that A and B are dependent if A and B are mutually exclusive and P(A) ≠ 0, P(B) ≠ 0.
Show that P(A|B) = 1 if B is a subset of A and P(B) ≠ 0.
A shipment of 60 game players, including 9 that are defective, is sent to a retail store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the
Use a graphing calculator to simulate 200 tosses of a nickel and dime, representing the outcomes HH, HT, TH, and TT by 1, 2, 3, and 4, respectively. (A) Find the empirical probabilities of the four
(A) Explain how a graphing calculator can be used to simulate 500 tosses of a coin.(B) Carry out the simulation and find the empirical probabilities of the two outcomes. (C) What is the probability
Suppose that 6 female and 5 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 11 finalists, what is the probability of selecting.(A) 3
Twelve popular brands of beer are used in a blind taste study for consumer recognition. (A) If 4 distinct brands are chosen at random from the 12 and if a consumer is not allowed to repeat any
There are 10 senators (half Democrats, half Republicans) and 16 representatives (half Democrats, half Republicans) who wish to serve on a joint congressional committee on tax reform. An 8-person
A town council has 9 members: 5 Democrats and 4 Republicans. A 3-person zoning committee is selected at random.(A) What is the probability that all zoning committee members are Democrats? (B) What
In Problems 27–30, simplify each expression assuming that n is an integer and n ≥ 2. (n + 3)! (n + 1)!
In Problems 31–36, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. (p→q) ^ (q→p)
Solve Problem 29 using permutations or combinations, whichever is applicable. Problem 29.How many seating arrangements are possible with 6 people and 6 chairs in a row? Solve using the
In Problems 31–36, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. PV (q→p)
In Problems 25–32, use the given information to complete the following table. n(A) = 175, n(B) = 125, n(AUB) = 300, n(U) n(U) = 300
In Problems 29–34, state the converse and the contrapositive of the given proposition.If n is an integer that is a multiple of 8, then n is an integer that is a multiple of 2 and a multiple of 4.
In Problems 31–36, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. (PV p) → (q^¬q)
In Problems 31–36, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. (b←d) v b
In Problems 33 and 34, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.(A) If A or B is the empty set, then A and B are
In Problems 35–52, construct a truth table for the proposition and determine whether the proposition is a contingency, tautology, or contradiction. -p ^ q

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