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- 6 Students are selected from a group of 14 students for different prizes. How many different possible group could be generated for the 6 students selected? Select one: a. 14!/8! b. 14!/6! c. 14!/(8!6!) d. 8! 6!Birth days. During a 2-month period in 2002, 72 babies were born at the Tompkins Community Hospital in up-state New York. The table shows how many babies were born on each day of the week. a) If births are uniformly dis-tributed across all days of the week, how many would youexpect on each day?b) Only 7 births occurred on aMonday. Does this indicate thatwomen might be less likelyto give birth on a Monday?Explain.c) Are the 17 births on Tuesdaysunusually high? Explain.d) Can you think of any reasons why births may notoccur completely at random? Day BirthsMon. 7Tues. 17Wed. 8Thurs. 12Fri. 9Sat. 10Sun. 95. In how many ways can five dogs and seven cats be ordered in a row? (For example, "dccdcdcddcce" is one such ordering.) 6. A coin is tossed fifteen times. a. How many sequences of heads and tails are possible? (e.g. "httttttthhhtht") b. How many sequences are possible that result in a total of two heads? (e.g. "ttthtttthtttttt") c. How many sequences are possible that result in a total of seven heads? 7. A die is rolled seven times. a. How many sequences of results are possible? (e.g. "5211523") b. How many sequences are possible that result in a total of six 3s? (e.g. "3333353") c. How many sequences are possible that result in a total of three 5s and two 6s? (e.g. "5265561") 8. A fair coin is tossed ten times. What is the probability of obtaining the following outcomes? # of heads: probability: 10 9 8 7 9. A fair coin is tossed fifty times. What is the probability of obtaining... a. fifty heads? b. twenty-five heads? 6 5 10. There are twelve calico cats and seven tabby cats. In how…
- How many permutations are there of 40 objects when taken 13 objects at a time, if a particular one of these objects must always be included? a. 13(40-1)!/(40-13-1)! b. 13(40 - 1)!/(40-13)! c. (40 - 1)!/(40-13-2)! d. 13(40)!/(40-13)! e. 40(40 - 1)!/(40-13-2)!Show All Work Please... Consider a deck of cards that has 80 cards. Of these, 60 have a color and 20 are “wild.” The 60 cards with a color are either red, yellow, green, or blue, with 15 of each color. Two cards are said to “match” if any of the following are true: they have the same color, one is a color and the other is wild, or both are wild. (This is a simplified version of the card game UNO.) Two cards are drawn from the well-shuffled deck without replacement. Express your answers to (a)-(d) as simplified fractions or as percentages rounded to the nearest hundredth of a percent. (a) What is the chance that both are blue? _________ (b) What is the chance that both are color cards and they are the same color? _________ (c) What is the chance that one is a color card and the other is wild? _________ (d) What is the chance that they match, using the definition above? _________ (e) Are the following two events mutually…11. In the Colorado Power Ball Lottery you choose 5 white numbered balls from a group of 75 and 1 red ball from a group of 15. How many possible winning combinations are there? How many winning combinations contain the white number 2 and 8? 3 of 3
- 27 A box contains 5 blue marbles, 3 green marbles, and 7 red marbles. How many marbles must be randomly drawn from the box to ensure that 1 of every colored marble have been drawn? O 11 13 3A coin is tossed three times, where (i) A: head on third toss, B: heads on first two tosses (ii) A: at least two heads, B: at most two heads (iii) A: at most two tails, B: at least one tail In each case find P(A/B).4. How many distinct permutations can be made from the word “DYNAMICS”?5. How many outcomes are possible from tossing a coin twice and rolling a 6-sideddie?6. How many ways are there to select 3 candidates from 15 equally qualified recentgraduates for opening in a law firm?
- An experiment involves 32 participants. From these, a group of 5 participants is to be tested under a special condition. How many groups of 5 participants are possible? (b) From a collection of 51 store customers, 2 are to be chosen to receive a special gift. How many groups of 2 customers are possible?8:18 l 5G Blackbo... EDIT •.. 10! 3628800 11! 39916800 12! 479001600 13! 6227020800 14! 87178291200 15! 1307674368000 16! 20922789888000 17! 355687428096000 18! 6402373705728000 19! 121645100408832000 20! 2432902008176640000 2) After a recent bank robbery, three eyewitnesses reported seeing a man with glasses flee the scene. The police suspect Ricky and make up an identity parade of five men with glasses. Ricky takes his place in the parade alongside four randomly chosen stooges. Two of the eyewitnesses identify Ricky and the third points to one of the stooges. What's the probability that Ricky would have been chosen by two of the three eyewitnesses if each witness had chosen completely at random? Solve this problem using the Binomial Probability Mass Function. (Tip: This problem 1 Applied Statistics (CRJ 504) will be easier to solve if you first find p, the probability of success on any one trial; in other words, the probability of a single eyewitness choosing Ricky) 3) Suppose test…4. In a lottery game where 4 numbers are chosen from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9), how many different 4-number cards could be made where: a) order is taken into consideration? b) order is not taken into consideration?
