问题1.明天下雨的概率为0.85。明天不下雨的概率是多少?
解决方案：
Let event of raining tomorrow be P (A)
The probability of raining tomorrow is P (A) = 0.85
Probability of not raining is given by P (A) = 1 – P (A)
Therefore, probability of not raining tomorrow = P (A) = 1 – 0.85
= 0.15
问题2.掷骰子。找到获得的可能性：
(i)质数
解决方案：
Outcomes of a die are 1, 2, 3, 4, 5, 5 and 6
Total outcomes = 6
Prime numbers are 1, 3 and 5
Favorable outcomes = 3
Probability of getting a prime number = Number of favorable outcomes/Total outcomes
= 3/6
= 1/2
Therefore, probability of getting a prime number = 1/2
(ii)2或4
解决方案：
Outcomes of a die are 1, 2, 3, 4, 5, 5 and 6
Total outcomes = 6
Favorable outcomes=2
Probability of getting 2 and 4 = Favorable outcomes/Total outcomes
= 2/6
= 1/3
Therefore, probability of getting 2 and 4 is 1/3
(iii)2或3的倍数
解决方案：
Outcomes of a die are 1, 2, 3, 4, 5, 5 and 6
Total outcomes = 6
Multiples of 2 and 3 are 2, 3, 4 and 6
Favorable outcomes = 4
Total number of multiples are 4
Probability of getting a multiple of 2 or 3 = Favorable outcomes/Total number of outcomes
= 4/6
= 2/3
Therefore, probability of getting a multiple of 2 or 3 is 2/3
问题3.在同时掷出一对骰子的过程中，求出获得以下几率的可能性：
(i)总和为8
解决方案：
Possible outcomes when a pair of dice is rolled are
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
(where first number shows the number on first dice and second number shows the number on second dice.)
Total number of outcomes = 36
Number of outcomes having 8 as sum are (6, 2), (5, 3), (4, 4), (3, 5) and (2, 6)
Numbers of favorable outcomes = 5
Probability of getting numbers of outcomes having 8 as sum = Favorable outcomes/Total outcomes
= 5/36
Therefore, probability of getting numbers of outcomes having 8 as sum is 5/36
(ii)一双
解决方案：
Total number of outcomes = 36
Number of outcomes as doublet are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6)
Number of favorable outcomes = 6
Probability of getting numbers of outcomes as doublet = Favorable outcomes/Total outcomes
= 6/36
= 1/6
Therefore, probability of getting numbers of outcomes as doublet is 1/6
(iii)质数的对偶
解决方案：
Total number of outcomes = 36
Number of outcomes as doublet of prime numbers are (1, 1), (3, 3), (5, 5)
Number of favorable outcomes = 3
Probability of getting numbers of outcomes as doublet of prime numbers = Favorable outcomes/Total outcomes
= 3/36
= 1/12
Therefore, probability of getting numbers of outcomes as doublet of prime numbers is 1/12
(iv)偶数的双数
解决方案：
Total number of outcomes = 36
Number of outcomes as doublet of odd numbers are (1, 1), (3, 3), (5, 5)
Number of favorable outcomes = 3
Probability of getting numbers of outcomes as doublet of odd numbers = Favorable outcomes/Total outcomes
= 3/36
= 1/12
Therefore, probability of getting numbers of outcomes as doublet of odd numbers is 1/12
(v)总和大于9
解决方案：
Total number of outcomes = 36
Number of outcomes having sum greater than 9 are (4, 6), (5, 5), (5, 6), (6, 6), (6, 4), (6, 5)
Number of favorable outcomes = 6
Probability of getting numbers of outcomes having sum greater than 9 = Favorable outcomes/Total outcomes
= 6/36
= 1/6
Therefore, probability of getting numbers of outcomes having sum greater than 9 is 1/6
(vi)第一个为偶数
解决方案：
Total number of outcomes = 36
Number of outcomes having an even number on first are:
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5) and (6, 6)
Number of favorable outcomes = 18
Probability of getting numbers of outcomes having an even number on first = Favorable outcomes/Total outcomes
= 18/36
= 1/2
Therefore, probability of getting numbers of outcomes having an even number on first is 1/2
(vii)一个数字为偶数，另一个数字为3的倍数
解决方案：
Total number of outcomes = 36
Number of outcomes having an even number on one and a multiple of 3 on the other are (2, 3), (2, 6), (4, 3), (4, 6), (6, 3) and (6, 6)
Number of favorable outcomes = 6
Probability of getting an even number on one and a multiple of 3 on the other is = Favorable outcomes/Total outcomes
= 6/36
= 1/6
Therefore, probability of getting an even number on one and a multiple of 3 on the other is 1/6
(viii) 9和11都不是面孔上数字的总和
解决方案：
Total number of outcomes = 36
Number of outcomes having 9 nor 11 as the sum of the numbers on the faces are (3, 6), (4, 5), (5, 4), (5, 6), (6, 3) and (6, 5)
Number of favorable outcomes for 9 nor 11 as the sum of the numbers on the faces are 6
Probability of getting 9 nor 11 as the sum of the numbers on the faces is = Favorable outcomes/Total outcomes
= 6/36
= 1/6
Probability of outcomes having 9 nor 11 as the sum of the numbers on the faces P (E) = 1/6
Probability of outcomes not having 9 nor 11 as the sum of the numbers on the faces is given by P (E) = 1 – 1/6 = (6 – 1)/5 = 5/6
Therefore, probability of outcomes not having 9 nor 11 as the sum of the numbers on the faces is 5/6
(ix)少于6的款项
解决方案：
Total number of outcomes = 36
Number of outcomes having a sum less than 6 are (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)
Number of favorable outcomes = 10
Probability of getting a sum less than 6 is = Favorable outcomes/Total outcomes
= 10/36
= 5/18
Therefore, probability of getting sum less than 6 is 5/18
(x)少于7的总和
解决方案：
Total number of outcomes = 36
Number of outcomes having a sum less than 7 are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)
Number of favorable outcomes = 15
Probability of getting a sum less than 7 is = Favorable outcomes/Total outcomes
= 15/36
= 5/12
Therefore, probability of getting sum less than 7 is 5/12
(xi)一笔超过7的款项
解决方案：
Total number of outcomes = 36
Number of outcomes having a sum more than 7 are
(2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Number of favorable outcomes = 15
Probability of getting a sum more than 7 is = Favorable outcomes/Total outcomes
= 15/36
= 5/12
Therefore, probability of getting sum more than 7 is 5/12
(xii)至少一次
解决方案：
Total number of outcomes = 36
Number of favorable outcomes =11
Probability of getting outcomes for at least once is = Favorable outcomes/Total outcomes
= 11/36
Therefore, probability of getting outcomes for at least once is 11/36
(xiii)任何骰子上不是5的数字。
解决方案：
Total number of outcomes = 36
Number of outcomes having 5 on any die are
(1, 5), (2, 5), (3, 5), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 5)
Number of favorable outcomes having 5 on any die = 15
Probability of getting 5 on any die is = Favorable outcomes/Total outcomes
= 11/36
Therefore, probability of getting 5 on any die is 11/36
Probability of not getting 5 on any die P (E) = 1 – P (E)
= 1 – 11/36
= (36 – 11)/36
= 25/36
Therefore, probability of not getting 5 on any die is 25/36
4.将三枚硬币扔在一起。找到获得的可能性：
(i)正好两个脑袋
解决方案：
Possible outcome of tossing three coins are HTT, HHT, HHH, HTH, TTT, TTH, THT, THH
Total outcomes = 8
Number of outcomes of exactly two heads are HHT,HTH,THH
Favorable outcomes = 3
Probability of getting exactly two heads is = Favorable outcomes/Total outcomes
= 3/8
Therefore, probability of getting exactly two heads is 3/8
(ii)至少两个首长
解决方案：
Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH
Total outcomes = 8
Number of outcomes of at least two heads are HHT,HHH,HTH,THH
Favorable outcomes = 4
Probability of getting at least two heads = Favorable outcomes/Total outcomes
= 4/8
= 1/2
Therefore, probability of getting at least two heads is 1/2
(iii)至少一头一尾
解决方案：
Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH
Total outcomes = 8
Number of outcomes of at least one head and one tail are HTT, HHT, HTH, TTH, THT, THH
Favorable outcomes = 6
Probability of getting at least one head and one tail = Favorable outcomes/Total outcomes
= 6/8
= 3/4
Therefore, probability of getting at least one head and one tail is 3/4
(iv)没有尾巴
解决方案：
Possible outcome of tossing three coins are: HTT, HHT, HHH, HTH, TTT, TTH, THT, THH
Total outcomes = 8
Number of outcomes of no tails are HHH
Favorable outcomes = 1
Probability of getting no tails = Favorable outcomes/Total outcomes
= 1/8
Therefore, probability of getting no tails is 1/8
问题5.从52张纸牌中随机抽取一张纸牌。找出开牌的概率为：
(i)黑人国王
解决方案：
Total number of cards are 52
Number of black king cards are 2
Probability of getting black king cards is = Favorable outcomes/Total outcomes
= 2/52
= 1/26
Therefore, probability of getting black king cards is 1/26
(ii)黑牌或国王
解决方案：
Total number of cards are 52
Number of either a black card or a king = 28
Probability of getting either a black card or a king is = Favorable outcomes/Total outcomes
= 28/52
= 7/13
Therefore, probability of getting either a black card or a king is 7/13
(iii)黑与王
解决方案：
Total number of cards are 52
Number of black and a king are 2
Probability of getting black and a king is = Favorable outcomes/Total outcomes
= 2/52
= 1/26
Therefore, probability of getting black and a king is 1/26
(iv)千斤顶，皇后或国王
解决方案：
Total number of cards are 52
Number of a jack, queen or a king = 12
Probability of getting a jack, queen or a king is = Favorable outcomes/Total outcomes
= 12/52
= 3/13
Therefore, probability of getting a jack, queen or a king is 3/13
(v)心与王
解决方案：
Total numbers of cards = 52
Total number of heart cards = 13
Probability of getting a heart is = Favorable outcomes/Total outcomes
= 13/52
= 1/4
Total number of king cards = 4
Probability of getting a king is = Favorable outcomes/Total outcomes
= 4/52
= 1/13
One card is common in heart and king (king of heart)
Total probability of getting a heart and a king = 1/4+ 1/13 – 1/52
= (13 + 4 – 1)/52
= (17 – 1)/52
= 16/52
= 4/13
Therefore, probability of getting neither a heart nor a king = 1 – 4/13 = (13 – 4)/13 = 9/13
(vi)锹或王牌
解决方案：
Total numbers of cards = 52
Number of spade cards = 13
Probability of getting spade cards is = Favorable outcomes/Total outcomes
= 13/52
= 1/4
Number of ace cards = 4
Probability of getting ace cards is = Favorable outcomes/Total outcomes
= 4/52
= 1/13
One card is common in both ace and spade (ace of spade) = 1/52
Probability of getting an ace or spade cards is = 1/4 + 1/13 – 1/52
= (13 + 4 – 1)/52
= (17 – 1)/52
= 16/52
= 4/13
Therefore, probability of getting an ace or spade cards is = 4/13
(vii)王牌和国王
解决方案：
Total numbers of cards = 52
Number of king cards = 4
Number of ace cards = 4
Total number of cards = 4 + 4 = 8
Total number of neither an ace nor a king are = 52 – 8 = 44
Probability of getting neither an ace nor a king is = Favorable outcomes/Total outcomes
= 44/52
= 11/13
Therefore, probability of getting neither an ace nor a king is 11/13
(viii)红牌或王后都不
解决方案：
Total numbers of cards = 52
Red cards include hearts and diamonds
Number of hearts in a deck of 52 cards = 13
Number of diamonds in a deck of 52 cards = 13
Number of queen in a deck of 52 cards = 4
Total number of red card and queen = 13 + 13 + 2 = 28 (since queen of heart and queen of diamond are already considered)
Number of card which is neither a red card nor a queen = 52 – 28 = 24
Probability of getting neither a king nor a queen is = Favorable outcomes/Total outcomes
= 24/52
= 6/13
Therefore, probability of getting neither a king nor a queen is 6/13
(ix)除王牌外
解决方案：
Total numbers of cards = 52
Total number of ace cards = 4
Total number of non-ace cards = 52 – 4 = 48
Probability of getting non-ace is = Favorable outcomes/Total outcomes
= 48/52
= 12/13
Therefore, probability of getting non-ace card is 12/13
(x)十
解决方案：
Total numbers of cards are 52
Total number of ten cards = 4
Probability of getting ten cards is = Favorable outcomes/Total outcomes
= 4/52
= 1/13
Therefore, probability of getting ten- card is 1/13
(xi)一把铁锹
解决方案：
Total numbers of cards = 52
Total number of spade cards = 13
Probability of getting spade is = Favorable outcomes/Total outcomes
= 13/52
= 1/4
Therefore, probability of getting a spade is 1/4
(xii)黑卡
解决方案：
Total numbers of cards = 52
Cards of spades and clubs are black cards.
Number of spades = 13
Number of clubs = 13
Total number of black card out of 52 cards = 13 + 13 = 26
Probability of getting black cards is = Favorable outcomes/Total outcomes
= 26/52
= 1/2
Therefore, probability of getting a black card is 1/2
(十三)七个俱乐部
解决方案：
Total numbers of cards = 52
Total number of the seven of club cards = 1
Probability of getting the seven of clubs cards is = Favorable outcomes/Total outcomes
= 1/52
Therefore, probability of the seven of club card is 1/52
(十四)杰克
解决方案：
Total numbers of cards = 52
Total number of jack cards = 4
Probability of getting jack cards is = Favorable outcomes/Total outcomes
= 4/52
= 1/13
Therefore, probability of the jack card is 1/13
(xv)黑桃王牌
解决方案：
Total numbers of cards = 52
Total number of the ace of spades cards = 1
Probability of getting ace of spade cards is = Favorable outcomes/Total outcomes
= 1/52
Therefore, probability of the ace of spade card is 1/52
(xvi)女王
解决方案：
Total numbers of cards = 52
Total number of queen cards = 4
Probability of getting queen cards is = Favorable outcomes/Total outcomes
= 4/52
= 1/13
Therefore, probability of a queen card is 1/13
(xvii)一颗心
解决方案：
Total numbers of cards = 52
Total number of heart cards = 13
Probability of getting queen cards is = Favorable outcomes/Total outcomes
= 13/52
= 1/4
Therefore, probability of a heart card is 1/4
(xviii)红牌
解决方案：
Total numbers of cards = 52
Total number of red cards = 13+13 = 26
Probability of getting queen cards is = Favorable outcomes/Total outcomes
= 26/52
= 1/2
Therefore, probability of a red card is 1/2
问题6.骨灰盒包含10个红球和8个白球。随机抽出一个球。找出画出的球是白色的概率。
解决方案：
Total number of red balls = 10
Total number of red white balls = 8
Total number of balls = 10 + 8 = 18
Probability of getting a white ball is = Total number of white balls/Total numbers of balls
= 8/18
= 4/9
Therefore, probability of a white ball is 4/9
问题7.一个袋子包含3个红球，5个黑球和4个白球。从袋子中随机抽出一个球。抽出球的几率是：
(i)白色?
解决方案：
Total numbers of red balls = 3
Number of black balls = 5
Number of white balls = 4
Total number of balls = 3 + 5 + 4 = 12
Probability of getting a white ball is = Total number of white balls/Total numbers of balls
= 4/12
= 1/3
Therefore, probability of a white ball is 1/3
(ii)红色?
解决方案：
Total numbers of red balls = 3
Number of black balls = 5
Number of white balls = 4
Total number of balls = 3 + 5 + 4 = 12
Probability of getting a red ball is = Total number of red balls/Total numbers of balls
= 3/12
= 1/4
Therefore, probability of a red ball is 1/4
(iii)黑色?
解决方案：
Total numbers of red balls = 3
Number of black balls = 5
Number of white balls = 4
Total number of balls = 3 + 5 + 4 = 12
Probability of getting a black ball is = Total number of black balls/Total numbers of balls
= 5/12
Therefore, probability of a black ball is 5/12
(iv)不是红色?
解决方案：
Total numbers of red balls = 3
Number of black balls = 5
Number of white balls = 4
Total number of Non -red balls = 5 + 4 = 9
Probability of getting a not red ball is = Total number of not red balls/Total numbers of balls
= 9/12
= 3/4
Therefore, probability of not a red ball is 3/4
问题8.从数字1、2、3，…，15中选择的数字是4的倍数的概率是多少?
解决方案：
Total numbers are 15
Multiples of 4 are 4, 8, 12
Favorable outcomes=3
Probability of getting a multiple of 4 is = Favorable outcomes/Total outcomes
= 3/15
= 1/5
Therefore, probability of getting multiples of 4 is 1/5
问题9.一个袋子包含6个红色，8个黑色和4个白色的球。随机抽出一个球。抽出的球不是黑色的概率是多少?
解决方案：
Total numbers of red balls = 6
Number of black balls = 8
Number of white balls = 4
Total number of balls = 6 + 8 + 4 = 18
Number of non-black balls are = 6 + 4 = 10
Probability of getting a non-black ball is = Total number of non-black balls/Total number of balls
= 10/18
= 5/9
Therefore, probability of getting a non-black ball is 5/9
问题10.一个袋子包含5个白色和7个红色的球。随机抽出一个球。抽出的球是白色的几率是多少?
解决方案：
Total numbers of red balls = 7
Number of white balls = 5
Total number of balls = 7 + 5 = 12
Probability of getting a non-white ball is = Total number of white balls/Total number of balls
= 5/12
Therefore, probability of getting a white ball is 5/12