1. Two cards are drawn from a well-shuffled ordinary deck of 52 cards. Find the probability that they are both aces if the first card is (a) replaced, (b) not replaced.
2. Find the probability of a 4 turning up at least once in two tosses of a fair die.

3. One bag contains 4 white balls and 2 black balls; another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that (a) both are white, (b) both are black,(c) one is white and one is black.

4. Box I contains 3 red and 2 blue marbles while Box II contains 2 red and 8 blue marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box I; if it turns up tails, a marble is chosen from Box II. Find the probability that a red marble is chosen.

5. A committee of 3 members is to be formed consisting of one representative each from labor, management, and the public. If there are 3 possible representatives from labor,2 from management, and 4 from the public, determine how many different committees can be formed

6. In how many ways can 5 differently colored marbles be arranged in a row?

7. In how many ways can 10 people be seated on a bench if only 4 seats are available?

8. It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

9. How many 4-digit numbers can be formed with the 10 digits 0,1,2,3,. . . ,9 if (a) repetitions are allowed, (b) repetitions are not allowed, (c) the last digit must be zero and repetitions are not allowed?

10. Four different mathematics books, six different physics books, and two different chemistry books are to be arranged on a shelf. How many different arrangements are possible if (a) the books in each particular subject must all stand together, (b) only the mathematics books must stand together?

11. Five red marbles, two white marbles, and three blue marbles are arranged in a row. If all the marbles of the same color are not distinguishable from each other, how many different arrangements are possible?

12. In how many ways can 7 people be seated at a round table if (a) they can sit anywhere,(b) 2 particular people must not sit next to each other?

13. In how many ways can 10 objects be split into two groups containing 4 and 6 objects, respectively?

14. In how many ways can a committee of 5 people be chosen out of 9 people?

15. Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways can this be done if (a) any mathematician and any physicist can be included, (b) one particular physicist must be on the committee, (c) two particular mathematicians cannot be on the committee?

16. How many different salads can be made from lettuce, escarole, endive, watercress, and chicory?

17. From 7 consonants and 5 vowels,how many words can be formed consisting of 4 different consonants and 3 different vowels? The words need not have meaning.

18. In the game of poker5 cards are drawn from a pack of 52 well-shuffled cards. Find the probability that (a) 4 are aces, (b) 4 are aces and 1 is a king, (c) 3 are tens and 2 are jacks, (d) a nine, ten, jack, queen, king are obtained in any order, (e) 3 are of any one suit and 2 are of another, (f) at least 1 ace is obtained.

19. Determine the probability of three 6s in 5 tosses of a fair die.

20. A shelf has 6 mathematics books and 4 physics books. Find the probability that 3 particular mathematics books will be together.

21. A and B play 12 games of chess of which 6 are won by A,4 are won by B,and 2 end in a draw. They agree to play a tournament consisting of 3 games. Find the probability that (a) A wins all 3 games, (b) 2 games end in a draw, (c) A and B win alternately, (d) B wins at least 1 game.

22. A and B play a game in which they alternately toss a pair of dice. The one who is first to get a total of 7 wins the game. Find the probability that (a) the one who tosses first will win the game, (b) the one who tosses second will win the game.

23. A machine produces a total of 12,000 bolts a day, which are on the average 3% defective. Find the probability that out of 600 bolts chosen at random, 12 will be defective.

24. The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9, respectively. Find the probability that in 20 years (a) both, (b) neither, (c) at least one, will be alive.

ok, I'll update this to 3 to 4 questions. Thanks!

In this lab assignment, students will demonstrate the abilities to: - Use functions in math module - Generate random floating numbers - Select a random element from a sequence of elements - Select a random sample from a sequence of elements (Python Programming)

NO BREAK STATEMENTS AND IF TRUE STATEMENTS PLEASE

Help with the (create) of a program to play Blackjack. In this program, the user plays against the dealer. Please do the following.

(a) Give the user two cards.

You can use the following statements to create a list of cards: cards = ("A","2","3","4","5","6","7","8","9","10","J","Q","K") Use the choice function of the random module twice to draw two cards. J, Q and K each has a value of 10. To make the program easier, A always has a value of 11. Display the two cards drawn and the total value. If the total is 21, display "Blackjack! You have won!" and end the game (You can use the exit() function to end the program).

(b) Use a loop to allow user to draw more cards. Every time a card is drawn, display the card and the updated total. If the total is 21, display "Blackjack! You have won!" and end the game. If the total is higher than 21, display "Bust! You have lost!" and end the game. Otherwise, let the user to decide to draw another card.

(c) Use a loop to draw cards for the dealer. Every time a card is drawn, display the card and the updated total. If the total is 21, display "Blackjack! Dealer has won!" and end the game. If the total is higher than 21, display "Bust! Dealer has lost!" and end the game. The dealer must continue to draw another card until the total is 17 or higher.

(d) If neither the dealer nor the user gets blackjack or bust, compare their totals. If the user's total is higher, display "You have won"; otherwise, display "dealer has won".

The followings are a few examples: Card drawn: 7 Player's Total: 7 Card drawn: 7 Player's Total: 14 Want another card? [y/n] y Card drawn: K Player's Total: 24 Bust! You have lost!

Card drawn: 4 Player's Total: 4 Card drawn: Q Player's Total: 14 Want another card? [y/n] y Card drawn: 3 Player's Total: 17 Want another card? [y/n] y Card drawn: 4 Player's Total: 21 Blackjack! You have won!

Card drawn: 9 Player's Total: 9 Card drawn: 10 Player's Total: 19 Want another card? [y/n] n Card drawn: 3 Dealer's Total: 3 Card drawn: Q Dealer's Total: 13 Card drawn: 10 Dealer's Total: 23 Bust! Dealer has lost!

Card drawn: 6 Player's Total: 6 Card drawn: A Player's Total: 17 Want another card? [y/n] n Card drawn: A Dealer's Total: 11 Card drawn: J Dealer's Total: 21 Blackjack! Dealer has won!

Card drawn: J Player's Total: 10 Card drawn: J Player's Total: 20 Want another card? [y/n] n Card drawn: 3 Dealer's Total: 3 Card drawn: K Dealer's Total: 13 Card drawn: 6 Dealer's Total: 19 Player's total: 20 Dealer's total: 19 You have won!

Card drawn: 10 Player's Total: 10 Card drawn: 10 Player's Total: 20 Want another card? [y/n] n Card drawn: 10 Dealer's Total: 10 Card drawn: K Dealer's Total: 20 Player's total: 20 Dealer's total: 20 Dealer has won!

NO BREAK STATEMENTS PLEASE NO IF TRUE STATEMENTS PLEASE

John is watching an old game show rerun on television called Let’s Make a Deal in which the contestant chooses a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $130, and behind the other is a round-the-world trip worth $8,500. The game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is the expected value of the selection? (Round answer to 2 decimal places, e.g. 15.25.) Expected value $ 2222.50 LINK TO TEXT What is the standard deviation of that selection? (Round answer to 2 decimal places, e.g. 15.25.) Standard deviation $

Match the term or phrase with the correct Phylum (Division)

1.possess chlorophyll b

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

2. constructed of little "pill-boxes"

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

3.body structure has distinct organs

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

4. possess phycoerythrin

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

5.possess chlorophyll a

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

6.have cell walls

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

7. Siphonocladous body form

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

8.produce up to 50% of the atmospheric oxygen

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

9. possess floridean starch as a storage product

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

10.possess conceptacles at the receptacle tips

A. phaeophyta b.chrysophyta (Bacillariophyta) c.chlorophyta D.All phyla E.Rhodophyta

1. Define the two major types of corporate stock. Discuss the characteristicsof each of the two types. How does an investor realise a returnon a stock investment?

2. “Shareholders of corporate stock may have claims to a company’s assets and income.”  Discuss and analyse this quote.

3. Using the Dividend Valuation Model, calculate the following: What is the value of a common stockthat paid a $1.50 dividend at the end of the last year and is expected to pay a cash dividend in the future. Dividends are expected to grow at 7% annually and the investor’s required rate of return is 11%.

Jiminy’s Cricket Farm issued a 20-year, 7 percent semiannual coupon bond 4 years ago. The bond currently sells for 104 percent of its face value. The company’s tax rate is 23 percent. The book value of the debt issue is $55 million. In addition, the company has a second debt issue, a zero coupon bond with 10 years left to maturity; the book value of this issue is $30 million, and the bonds sell for 58 percent of par. a. What is the company’s total book value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.) b. What is the company’s total market value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.) c. What is the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

3. The megaspore in most flowering plants grows into a megagametophyte that has seven cells and eight nuclei. Name the seven cells.

4. After pollen lands on a stigma, it is far away from the ovule with the megagametophyte which holds the egg (the mega-gamete). How are the two sperm cells transported from the stigma to the egg?

5. After pollination and fertilization, as the ovule develops into a seed, the ovary matures into a ____________. Many of these have three parts, the _____________ is the skin or peel, the ___________is the flesh, and the innermost layer, the _____________, may be tough like the pit of a cherry.

During Thanksgiving you participated in a pumpkin-pie eating contest. You really enjoyed the first two pies, the third one was okay, but as soon as you ate the fourth one you became ill and lost the contest.

• Did your total utility increase or decrease with the first three pies you ate?.

• After the third pie, did your total utility increase or decrease?

• Did you get more or less utility from eating the first pie than from eating the third pie?

• Did you get more or less utility from eating the fourth pie than from eating the second pie?

A student council consists of 15 students.

(a)

In how many ways can a committee of five be selected from the membership of the council?

(b)

Two council members have the same major and are not permitted to serve together on a committee. How many ways can a committee of five be selected from the membership of the council?

(c)

Two council members always insist on serving on committees together. If they can't serve together, they won't serve at all. How many ways can a committee of five be selected from the council membership?

(d)

Suppose the council contains eight men and seven women.

(i)

How many committees of six contain three men and three women?

(ii)

How many committees of six contain at least one woman?

(e)

Suppose the council consists of three freshmen, four sophomores, three juniors, and five seniors. How many committees of eight contain two representatives from each class?

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.

• Part (a)

  In words, define the random variable X.

  the time (in seconds) per lapthe time (in seconds) per race    the distance (in miles) of each racethe distance (in miles) of each lap

• Part (b)

  Give the distribution of X.
  X ~

• Part (c)

  Find the percent of her laps that are completed in less than 135 seconds. (Round your answer to two decimal places.)
  

• Part (d)

  The fastest 2% of her laps are under how many seconds? (Round your answer to two decimal places.)
  sec

• Part (e)

  Enter your answers to two decimal places.
  
  The middle 80% of her lap times are from  seconds to  seconds.