[考古] 機率論/游景盛/972第二章小考
[開課學院]: 資電學院(ex:金融學院,商學院,理工學院,資電學院,建設學院,文學院...)
[開課系所]: 資訊系(ex:中文系,外文系,電機系,財稅系..)
[課程名稱]: 機率論
[老師名稱]: 游景盛 老師
[開課學期]: 972
[類型]: 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
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