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nature of mathematics

Questions and Answers of Nature Of Mathematics

Three fair coins are tossed. What is the probability that at least one is a head?
Find the probability of obtaining at least one head in four flips of a coin.
What are the odds in favor of drawing an ace from an ordinary deck of cards?
What are a four-child family's odds against having four boys?
The probability of drawing a heart from a deck of cards is \(\frac{1}{4}\); what are the odds against drawing a heart?
Suppose the probability of an event is 0.80 . What are the odds in favor of this event?
The odds against an event are ten to one. What is the probability of this event?
Racetracks quote the approximate odds for each race on a large display board called a tote board.Here's what it might say for a particular race:What would be the probability of winning for each of
Suppose the odds in favor are 9 to 1 that a man will be bald by the time he is 60 . State this as a probability.
Suppose the odds are 33 to 1 that someone will lie to you at least once in the next seven days. State this as a probability.
Suppose that a family wants to have four children.a. What is the sample space?b. What is the probability of 4 girls? 4 boys?c. What is the probability of 1 girl and 3 boys? 1 boy and 3 girls?d. What
What is the probability of obtaining exactly three heads in four flips of a coin, given that at least two flips are heads?
The all-girl Braxton family had a reality series on the WE network.a. What is the probability of a 6-child family having 6 boys?b. What is the probability that the next child of the Braxton family
The Emory Harrison family of Tennessee had 13 boys.a. What is the probability of a 13-child family having 13 boys?b. What is the probability that the next child of the Harrison family will be a boy
A single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen, or king.\(P(\)
A single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen, or king.\(P(\)
A single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen, or king.\(P\)
A single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen, or king.\(P\)
A single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen, or king.\(P(\)
A single card is drawn from a standard deck of cards. Find the probabilities if the given information is known about the chosen card in Problems 31-36. A face card is a jack, queen, or king.\(P(\)
Two cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in
Two cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in
Two cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in
Two cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in
Two cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in
Two cards are drawn from a standard deck of cards, and one of the two cards is noted and removed. Find the probabilities of the second card, given the information about the removed card provided in
What is the probability of getting a license plate that has a repeated letter or digit if you live in a state in which license plates have two letters followed by four numerals?
What is the probability of getting a license plate that has a repeated letter or digit if you live in a state in which license plates have one numeral followed by three letters followed by three
Consider the following table showing the results of a survey of TV network executives.Suppose one network executive is selected at random. Find the indicated probabilities.a. What is the probability
Suppose a single die is rolled. Find the probabilities.a. 6 , given that an odd number was rolledb. 5 , given that an odd number was rolledc. odd, given that the rolled number was a 6d. odd, given
Birthday Problem (extended) Rework Example 8 but do not exclude leap years. Is 23 still the number of people for which the probability of a match first exceeds \(50 \%\).
A group of four people is selected at random. What is the probability that at least two of them has the same birthday?
Suppose a pair of dice are rolled. Consider the sum of the numbers on the top of the dice and find the probabilities.a. 7 , given that the sum is oddb. odd, given that a 7 was rolledc. 7 , given that
Suppose a pair of dice are rolled. Consider the sum of the numbers on the top of the dice and find the probabilities.a. 5 , given that exactly one die came up 2b. 3 , given that exactly one die came
Suppose a pair of dice are rolled. Consider the sum of the numbers on the top of the dice and find the probabilities.a. 8 , given that a double was rolledb. a double, given that an 8 was rolled
Show that the odds against an event \(E\) can be found by computing \(P(\bar{E}) / P(E)\) .
Two cards are drawn from a deck of cards. Find the requested probabilities.a. The first card drawn is a club.b. The first card drawn is not a club.c. The second card drawn is a club if the first card
A sorority has 35 members, 25 of whom are full members and 10 of whom are pledges. Two persons are selected at random from the membership list of the sorority. Find the requested probabilities.a. The
Consider this letter to Dear Abby.a. What is the family's probability of having eight girls in a row?b. What are the odds against?c. Critique the doctor's comments, as reported by the letter's
The odds against winning a certain lottery are a million to one. Make up an example to help visualize these odds.
The odds against winning a certain lottery are ten million to one. Make up an example to help visualize these odds.
The odds against winning a certain "Power Ball" lotto are 150 million to 1. Make up an example to help visualize these odds.
One betting system for roulette is to bet \(\$ 1\) on black. If black comes up on the first spin of the wheel, you win \(\$ 1\) and the game is over. If black does not come up, double your bet \(\$
"Last week I won a free Big Mac at McDonald's. I sure was lucky!" exclaimed Charlie. "Do you go there often?" asked Pat. "Only twenty or thirty times a month. And the odds of winning a Big Mac were
What do we mean by independent events?
What is the formula for the probability of an intersection?
What is the formula for the probability of a union?
What is a finite stochastic process?
Suppose events A, B, and C are independent and\[P(A)=\frac{1}{2} \quad P(B)=\frac{1}{3} \quad P(C)=\frac{1}{6}\]Find the probabilities in Problems 5-12.a. \(P(\bar{A})\)b. \(P(\overline{A \cap B})\)
Suppose events A, B, and C are independent and\[P(A)=\frac{1}{2} \quad P(B)=\frac{1}{3} \quad P(C)=\frac{1}{6}\]Find the probabilities in Problems 5-12.a. \(P(\bar{B})\)b. \(P(\overline{A \cap C})\)
Suppose events A, B, and C are independent and\[P(A)=\frac{1}{2} \quad P(B)=\frac{1}{3} \quad P(C)=\frac{1}{6}\]Find the probabilities in Problems 5-12.a. \(P(\bar{C})\)b. \(P(\overline{B \cap C})\)
Suppose events A, B, and C are independent and\[P(A)=\frac{1}{2} \quad P(B)=\frac{1}{3} \quad P(C)=\frac{1}{6}\]Find the probabilities in Problems 5-12.a. \(P(A \cup B)\)b. \(P(\overline{A \cup B})\)
Suppose events A, B, and C are independent and\[P(A)=\frac{1}{2} \quad P(B)=\frac{1}{3} \quad P(C)=\frac{1}{6}\]Find the probabilities in Problems 5-12.a. \(P(A \cup C)\)b. \(P(\overline{A \cup C})\)
Suppose events A, B, and C are independent and\[P(A)=\frac{1}{2} \quad P(B)=\frac{1}{3} \quad P(C)=\frac{1}{6}\]Find the probabilities in Problems 5-12.a. \(P(B \cup C)\)b. \(P(\overline{B \cup C})\)
Suppose events A, B, and C are independent and\[P(A)=\frac{1}{2} \quad P(B)=\frac{1}{3} \quad P(C)=\frac{1}{6}\]Find the probabilities in Problems 5-12.\(P[(A \cup B) \cap C]\)
Suppose events A, B, and C are independent and\[P(A)=\frac{1}{2} \quad P(B)=\frac{1}{3} \quad P(C)=\frac{1}{6}\]Find the probabilities in Problems 5-12.\(P(\overline{A \cap B \cap C})\)
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
In Problems 13-24, suppose a die is rolled twice and let\[\begin{array}{ll}A=\{\text { first toss is a prime }\} & B=\{\text { first toss is a } 3\} \\C=\{\text { second toss is a } 2\} & D=\{\text {
Use the following tree diagram to answer the questions in Problems 25-30.Which path number represents \(P\left(D \mid A_{2}ight)\) ? A A2 A3 D D D D D D Path number 1 2 3 4 5 6
Use the following tree diagram to answer the questions in Problems 25-30.Which path number represents \(P\left(\bar{D} \mid A_{3}ight)\) ? A A2 A3 D D D D D D Path number 1 2 3 4 5 6
Use the following tree diagram to answer the questions in Problems 25-30.Describe path 1 as a probability. A A2 A3 D D D D D D Path number 1 2 3 4 5 6
Use the following tree diagram to answer the questions in Problems 25-30.Find \(P\left(\bar{D} \mid A_{2}ight)\). A A2 A3 D D D D D D Path number 1 2 3 4 5 6
Use the following tree diagram to answer the questions in Problems 25-30.Find \(P\left(D \mid A_{1}ight) \cdot P\left(A_{1}ight)\). A A2 A3 D D D D D D Path number 1 2 3 4 5 6
Use the following tree diagram to answer the questions in Problems 25-30.Find \(P\left(A_{2} \cap Dight)\). A A2 A3 D D D D D D Path number 1 2 3 4 5 6
Use the following tree diagram to answer the questions in Problems 31-36.Which path number represents \(P\left(C_{1} \mid B_{2}ight)\) ? B B B3 C C C C C C2 C3 Path number 1 2 3 4 5 6 7
Use the following tree diagram to answer the questions in Problems 31-36.Which path number represents \(P\left(C_{2} \mid B_{1}ight)\) ? B B B3 C C C C C C2 C3 Path number 1 2 3 4 5 6 7
Use the following tree diagram to answer the questions in Problems 31-36.Describe path 7 as a probability. \(P\left(B_{3} \cap C_{3}ight)\) B B B3 C C C C C C2 C3 Path number 1 2 3 4 5 6 7
Use the following tree diagram to answer the questions in Problems 31-36.Find \(P\left(C_{2} \mid B_{1}ight)\). B B B3 C C C C C C2 C3 Path number 1 2 3 4 5 6 7
Use the following tree diagram to answer the questions in Problems 31-36.Find \(P\left(C_{1} \mid B_{2}ight) \cdot P\left(B_{2}ight)\). B B B3 C C C C C C2 C3 Path number 1 2 3 4 5 6 7
Use the following tree diagram to answer the questions in Problems 31-36.Find \(P\left(B_{2} \cap C_{2}ight)\). B B B3 C C C C C C2 C3 Path number 1 2 3 4 5 6 7
A certain slot machine has three identical independent wheels, each with 13 symbols as follows: 1 bar, 2 lemons, 2 bells, 3 plums, 2 cherries, and 3 oranges. Suppose you spin the wheels and one of
Suppose a slot machine has three independent wheels as shown in Figure 13.10 on the following page. Find the probabilities.a. \(P(3\) bars)b. \(P(3\) bells )c. \(P(3\) cherries )d. \(P\) (cherries on
The one coin payoffs for the slot machine shown in Problem 37 are as follows:What is the mathematical expectation for playing the game with the coin being a dollar? Assume the three wheels are
The one coin payoffs for the slot machine shown in Figure 13.10 are as follows:Figure 13.10 First one cherry First two cherries First two wheels are cherries and the third wheel is a bar Three
A "high rollers" Keno is offered in which you pay \(\$ 749\) to play a one-spot ticket. If you catch your number, you are paid \(\$ 2,247\). What is your expectation for this game?
A special "catch all" Keno ticket allows you to play a six-spot ticket that pays only if you pick all 6 numbers. It costs \(\$ 5\) to play and pays \(\$ 27,777\) if you win. What is your expectation
What is the expectation for playing Keno by picking two numbers and paying \(\$ 1.00\) to play? The payoff for picking two numbers is \(\$ 12.00\).
What is the expectation for playing a four-spot Keno and paying \(\$ 5.00\) to play? The payoffs are \(\$ 565\) if you catch four, \(\$ 15\) if you catch four, and \(\$ 5\) if you catch two.
What is the probability of obtaining five tails when a coin is flipped five times?
What is the probability of obtaining at least one tail when a coin is flipped five times?
Assume a jar has five red marbles and three black marbles. Draw out two marbles with and without replacement. Find the requested probabilities.a. \(P\) (two red marbles)b. \(P\) (two black marbles)c.
Suppose that in an assortment of 20 calculators there are 5 with defective switches. Draw with and without replacement.a. If one machine is selected at random, what is the probability it has a
a. A game consists of at most three cuts with a deck of 52 cards. You win \(\$ 1\) and the game is over if a heart turns up, but lose \(\$ 1\) otherwise. Should you play?b. Repeat this game, but
a. A game consists of removing a card from a deck of 52 cards. If the card is a face card, you win \(\$ 1\) and the game is over. If it is not a face card, remove another card. If that one is a face
Compare and contrast the following two betting schemes for roulette, which are sometimes used by gamblers.Double on each loss Bet \(\$ 1\) on black. If black comes up, you win \(\$ 1\), and the game
Many states conduct lotteries; a typical lottery (Keno) payoff ticket is shown here. Assume there are 20 numbers chosen from a set of 80 possible numbers. Use this information for Problems 52-56.What
Many states conduct lotteries; a typical lottery (Keno) payoff ticket is shown here. Assume there are 20 numbers chosen from a set of 80 possible numbers. Use this information for Problems 52-56.What
Many states conduct lotteries; a typical lottery (Keno) payoff ticket is shown here. Assume there are 20 numbers chosen from a set of 80 possible numbers. Use this information for Problems 52-56.What
Many states conduct lotteries; a typical lottery (Keno) payoff ticket is shown here. Assume there are 20 numbers chosen from a set of 80 possible numbers. Use this information for Problems 52-56.What
Many states conduct lotteries; a typical lottery (Keno) payoff ticket is shown here. Assume there are 20 numbers chosen from a set of 80 possible numbers. Use this information for Problems

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