问题19.五张牌-十张，千斤顶，王后，国王和一张王牌钻石朝下摆放。随机选择一张卡。
(i)这张卡是皇后的概率是多少?
解决方案：
Total cards = 5
Total queen = 1
Number of favorable outcomes = 1
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of getting cards which is a queen = 1/5
(ii)如果首先抽出一张国王并放在一边，那么第二张被抽中的几率是
(a)王牌?
解决方案：
Total cards after king = 4
Number of favorable outcomes = 1
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of getting an ace card = 1/4
(b)国王?
解决方案：
Number of favorable outcomes = 0
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of getting a king = 0
问题20.一个袋子包含3个红球和5个黑球。从袋子中随机抽出一个球。抽出球的几率是：
(i)红色
解决方案：
Total number of balls = 3 + 5 = 8
Total red balls = 3
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of drawing a red ball = 3/8
(ii)返回
解决方案：
Total black ball = 5
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of drawing a black ball = 5/8
问题21.机会游戏包括旋转箭头，箭头同样有可能静止指向数字1、2、3，….，12中的一个，如图所示。它指向以下几率的可能性是多少?
(i)10?
解决方案：
Total numbers on the spin = 12
Favorable outcomes = 1
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of getting a 10 = 1/12
(ii)奇数?
解决方案：
Favorable outcomes are 1, 3, 5, 7, 9, and 11
Favorable outcomes = 6
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of getting a prime number = 6/12 = 1/2
(iii)3的倍数?
解决方案：
Favorable outcomes are 3, 6, 9, and 12
Favorable outcomes = 4
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of getting multiple of 3 = 4/12 = 1/3
(iv)偶数?
解决方案：
Favorable outcomes are 2, 4, 6, 8, 10, and 12
Favorable outcomes = 6
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of getting an even number = 6/12 = 1/2
问题22：在一堂课中，有18个女孩和16个男孩。班主任想选一个学生做班长。她所做的是，她将每个学生的名字写在卡片上，然后将它们放入篮子并充分混合。一个孩子被要求从篮子里捡一张卡片。卡上写的名字的几率是：
(i)一个女孩的名字
解决方案：
Total number of students in the class = 18 + 16 = 34
Favorable cases = 18
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of getting a name of girl on the card = 18/34 = 9/17
(ii)男孩的名字?
解决方案：
Favorable cases = 16
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of getting a name of boy on the card = 16/34 = 8/17
问题23：为什么抛硬币被认为是决定在板球比赛中哪支球队应该选择终点的一种公平方法?
解决方案：
Possible outcomes while tossing a coin = 2 (1 head or 1 tail)
Probability = Number of favorable outcomes/ Total number of outcomes
P(getting head) = 1/2
P(getting tail) = 1/2
As the probability of both the events are equal
Therefore, tossing a coin is considered to be a fair way of deciding which team should choose ends in a game of cricket.
问题24.从数字1、2、2、3、3、3、4、4、4、4中随机选择的数字是其平均值的概率是多少?
解决方案：
Total number of possible outcomes = 10
Average of the outcomes = (1 + 2 + 2+3+3+3+4+4+4+4) / 10
= 30/10
= 3
Let E be the event of getting 3.
Number of favorable outcomes = 3
P(E) = Number of favorable outcomes/ Total number of outcomes
P(E) = 3/10
Therefore, the probability that a number selected at random will be the average is 3/10.
问题25.一个袋子里有30张相同大小的卡片，上面写着1到30的数字。随机从包中取出一张卡。找出所选卡上的数字不能被3整除的概率。
解决方案：
Total number of possible outcomes are 30 {1, 2, 3, … 30}
Let E = event of getting a number that is divisible by 3
Number of favorable outcomes = 10{3, 6, 9, 12, 15, 18, 21, 24, 27, 30}
Probability, P(E) = Number of favorable outcomes/ Total number of outcomes
P(E) = 10/30
= 1/3
P(not E) = 1- 1/3
= 2/3
Therefore, the probability that the number on the selected card is not divisible by 3 = 2/3
问题26.一个袋子包含5个红色，8个白色和7个黑色的球。从袋子中随机抽出一个球。找出被抽出的球是
解决方案：
(i) red or white
Total number of possible outcomes = 20 (5 red, 8 white & 7 black}
Number of favorable outcomes = 13 (5 red + 8 white)
Probability = Number of favorable outcomes/ Total number of outcomes
Therefore, the probability of red or white ball = 13/20
(ii) not black
No. of favorable outcomes =7 (7 black balls)
Probability = Number of favorable outcomes/ Total number of outcomes
Probability of black ball = 7/20
= 7/20
P (not E) = 1-7/20
= 13/20
(iii) neither white nor black.
Number of favorable outcomes = 20 – 8 – 7 = 5(total balls – no. of white balls – no. of black balls)
Probability = Number of favorable outcomes/ Total number of outcomes
P(E) = 5/20 = 1/4
问题27.在每个给定数字被选择的可能性相同的情况下，找到从数字1到25中选择的数字不是质数的可能性。
解决方案：
Total no. of possible outcomes = 25 {1, 2, 3…. 25}
Favorable outcomes are 2, 3, 5, 7, 11, 13, 17, 19, 23
Number. of favorable outcomes = 9
Probability= Number of favorable outcomes/ Total number of outcomes
P(E) = 9/25
P(not E) = 1-9/25
= 16/25
Therefore, the probability of selecting a number which is not prime is 16/25.
问题28.一个袋子包含8个红色，6个白色和4个黑色的球。从袋子中随机抽出一个球。找出被抽出的球是
(i)红色或白色
解决方案：
Total number of balls = 8 + 6 + 4 = 18
Total outcomes =18
Favorable outcomes = 14 (8 red balls + 6 white balls)
Probability = Number of favorable outcomes/ Total number of outcomes
= 14/18
= 7/9
(ii)不是黑色
解决方案：
Let E be event of getting a black ball
Number of favorable outcomes = 4
P(E) = 4/18
P(E) = 2/9
P(not E) = 1-2/9
= 7/9
Therefore, probability of not a black ball is 7/9
(iii)白色或黑色
解决方案：
Let E be event of getting neither a white nor a black ball
Favorable outcomes = 18 – 6 – 4
= 8
Probability= Number of favorable outcomes/ Total number of outcomes
P(E) = 8/18 = 4/9
问题29：找出从数字1、2、3…中随机选择一个数字的概率。 35是：
(i)素数
解决方案：
Total outcomes = 35
Favorable outcomes =11 {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31)
Probability = Number of favorable outcomes/ Total number of outcomes
= 11/35
Therefore, the probability of prime number = 1/22
(ii)7的倍数
解决方案：
Favorable outcomes = 5 {7, 14, 21, 28, 35}
Probability = Number of favorable outcomes/ Total number of outcomes
= 5/35
= 1/7
Therefore, the probability of multiple of 7 = 1/22
(iii)3或5的倍数
解决方案：
Favorable outcomes = 16 {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 5, 10, 20, 25, 35}
Probability = Number of favorable outcomes/ Total number of outcomes
= 16/35
Therefore, the probability of multiple of 3 or 5= 1/22
问题30.从52张纸牌中取出红色的杰克，皇后，国王和王牌。从剩余的部分中随机抽出一张牌。找出开出的纸牌的几率
(i)黑人女王
解决方案：
Total cards = 52
All jacks, queens & kings, ace of red color are removed.
Total outcomes = 52 – 2 – 2 – 2 – 2 = 44 (remaining cards)
Favorable outcomes = 2 (queen of spade & club)
Probability = Number of favorable outcomes/ Total number of outcomes
= 2/44
=1/22
Therefore, the probability of black queen = 1/22
(ii)红牌
解决方案：
Favorable outcomes = 26 – 8
= 18
Probability = Number of favorable outcomes/ Total number of outcomes
= 18/44
= 9/22
Therefore, the probability of red card = 1/22
(iii)一个黑杰克
解决方案：
Favorable outcomes = 2 (jack of club & spade)
Probability = Number of favorable outcomes/ Total number of outcomes
= 2/44
= 1/22
Therefore, the probability of black jack = 1/22
(iv)图片卡(夹克，皇后和国王是图片卡)
解决方案：
Favorable outcomes = 6 (2 jacks, 2 kings & 2 queens of black color)
Probability = Number of favorable outcomes/ Total number of outcomes
= 6/44
= 3/22
Therefore, the probability of picture card = 3/22
问题31.一个袋子仅包含柠檬味的糖果。马里尼不看袋子就拿出一个糖果。她取出的几率是多少：
(i)橙味糖果
解决方案：
Taking out orange flavored candy is an impossible event because all lemon candies are there.
Therefore, probability = 0
(ii)柠檬味糖果
解决方案：
As the bag contains all lemon candies, taking out lemon candy is sure event
Therefore, probability = 1
问题32.假定在3名学生的组中，有2名学生没有相同生日的概率为0.992。这两个学生有相同生日的概率是多少?
解决方案：
E = event of 2 students not having same birthday
P(E) = 0.992
P(not E) = 1 – 0.992
= 0.008
Therefore, the probability that the 2 students have the same birthday is 0.008
问题33.一个袋子包含3个红球和5个黑球。从袋子中随机抽出一个球。抽出球的几率是多少
(i)红色
解决方案：
Total outcomes = 8
Favorable outcomes = 3
Probability = Number of favorable outcomes/ Total number of outcomes
= 3/8
Therefore, the probability of red ball = 3/8
(ii)不是红色
解决方案：
P(not red) = 1- P(red)
= 1-3/8
=5/8
Therefore, the probability of not red ball = 5/8
问题34.一个盒子装有5个红色大理石，8个白色大理石和4个绿色大理石。随机从包装盒中取出一种大理石。取出大理石的概率是多少
(i)红色
解决方案：
Total outcomes = 17
Favorable outcomes = 5
Probability = Number of favorable outcomes/ Total number of outcomes
= 5/17
Therefore, the probability of red marble = 5/17
(ii)不是绿色
Favorable outcomes = 4
Probability = Number of favorable outcomes/ Total number of outcomes
= 4/17
P(not green) = 1 – 4/17
= 13/17
Therefore, the probability that the marble taken out is not green is 13/17.
问题35.一支笔包括144支圆珠笔，其中20支有缺陷，而其他则为好。 Nuri会买一支好笔，但如果有缺陷则不会买。店主随机抽一支笔给她。概率是多少
(i)她会买的
解决方案：
Good pens = 144 – 20 = 124
Defective pens = 20
Total outcomes =144
Favorable outcomes = 124
Probability = Number of favorable outcomes/ Total number of outcomes
= 124/144
= 31/36
Therefore, the probability that she will buy = 31/36
(ii)她不会购买
解决方案：
P(buying it) = 31/36
P(not buying it) = 1-31/36
=5/36
Therefore, the probability that she will not buy = 5/36
问题36：12支有缺陷的笔意外地与132支好笔混合在一起。不能只看笔并判断它是否有缺陷。从这批中随机抽出一支笔。确定笔拿出好笔的概率。
解决方案：
Good pens = 132
Defective pens = 12
Total outcomes = 144
Favorable outcomes = 132
Probability = Number of favorable outcomes/ Total number of outcomes
= 132/144
= 11/12
Therefore, probability of good pen = 11/12