[开课学院]: 资电学院(ex:金融学院,商学院,理工学院,资电学院,建设学院,文学院...) [开课系所]: 资讯系(ex:中文系,外文系,电机系,财税系..) [课程名称]: 机率论 [老师名称]: 游景盛 老师 [开课学期]: 972 [类型]: 第二章小考ex:(第n次)小考/98-2期中考/98-2期末考 1.In how many ways can we draw five cards from an ordinary deck of 52 cards (a) with replacement;(b) without replacement? (a)52^5 (b)52x51x50x49x48 2.How many divisors does 55,125 have? Hint: 5,125=3^2x5^3x7^2. 3x4x3=36 3.A campus telephone extension has four digits. How many different extensions with no repeated digits exist? Of these.(a) how many do not start with a 0; (b) how many do not have 01 as the first two digits? 10x9x8x7=5040 (a)9x9x8x7 (b)5040-(1x1x8x7) 4.Professor Haste is somewhat familar with six languages. To translate texts from one language into another directly. how many one-way dictionaries does he need? 6P2=6!/4! 5.A dancing contest has 11 competitors, of whom three are Americans, two are Mexican, three are Russians, and three are Italians. If the contest result lists only the nationlity of the dancers, how many outcomes are possible? 11!/(3!2!3!3!) 6.A fair die is tossed eight times. What is the probability of exactly two 3's, exactly three 1's, and exactly two 6's? (3x(8!/(2!3!2!)))/6^8 7.A fair die is tossed six times. What is the probability of getting exactly two 6's? 6 P(A)=(( )x5^4)/6^6 2 8.What is the coefficient of x^3y^7 in the expansion of (2x-y+3)^13? 13!/(3!7!3!) 9.An ordinary deck of 52 cards is divided into two equal sets randomly. What is the probability that each set contains exactly 13 red cards? 26 26 52 (( )( ))/( ) 13 13 26 10.Judy has three sets of classics in literature, each set having four volumes. In how many ways can she put them on a bookshelf so that books of each set are not separated? 3!4!4!4! 11.In a bridge game, each of the four players gets 13 random cards. What is the probability that every player has an ace? 4 48 3 36 2 24 1 12 (( )( )( )( )( )( )( )( ))/(52!/13!13!13!13!) 1 12 1 12 1 12 1 12 --

※ 发信站: 批踢踢实业坊(ptt.cc) ◆ From: 114.46.152.141