第26章数据处理IV(概率)–练习26.1 |套装1
问题11.一个袋子包含4个红色，5个黑色和6个白色的球。从袋子中随机抽出一个球。找出被抽出的球的概率为：
(i)白色
解决方案：
Number of red balls = 4
Number of black balls = 5
Number of white balls = 6
Total number of balls = 4 + 5 + 6 = 15
Probability of getting a white ball = Favorable outcomes/Total outcomes
= 6/15
= 2/5
Therefore, probability of getting a white ball is 2/5
(ii)红色
解决方案：
Number of red balls = 4
Number of black balls = 5
Number of white balls = 6
Total number of balls = 4 + 5 + 6 = 15
Probability of getting a red ball = Favorable outcomes/Total outcomes
= 4/15
Therefore, probability of getting a white ball is 4/15
(iii)不是黑色
解决方案：
Number of red balls = 4
Number of black balls = 5
Number of white balls = 6
Total number of balls = 4 + 5 + 6 = 15
Number of non-black balls = 4 + 6 = 10
Probability of getting a non-black ball = Favorable outcomes/Total outcomes
= 10/15
= 2/3
Therefore, probability of getting a non-black ball is 2/3
(iv)红色或白色
解决方案：
Number of red balls = 4
Number of black balls = 5
Number of white balls = 6
Total number of balls = 4 + 5 + 6 = 15
Number of red and white balls = 4 + 6 = 10
Probability of getting a red or white ball = Favorable outcomes/Total outcomes
= 10/15
= 2/3
Therefore, probability of getting a red or white ball is 2/3
问题12.一个袋子包含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：
Number of red balls = 3
Number of black balls = 5
Total number of balls = 3 + 5 = 8
Probability of getting a red ball is = Favorable outcomes/Total outcomes
= 3/8
Therefore, probability of getting a red ball is 3/8
(ii)黑色
解决方案：
Number of red balls = 3
Number of black balls = 5
Total number of balls = 3 + 5 = 8
Probability of getting a black ball = Favorable outcomes/Total outcomes
= 5/8
Therefore, probability of getting a black ball is 5/8
问题13：一个袋子包含5个红色大理石弹，8个白色大理石弹，4个绿色大理石弹。如果随机从包中取出一种大理石，该概率是多少?
(i)红色
解决方案：
Number of red marbles = 5
Number of white marbles = 8
Number of green marbles = 4
Total number of marbles = 5 + 8 + 4 = 17
Probability of getting a red marble = Favorable outcomes/Total outcomes
= 5/17
Therefore, probability of getting a red marble is 5/17
(ii)白色
解决方案：
Number of red marbles = 5
Number of white marbles = 8
Number of green marbles = 4
Total number of marbles = 5 + 8 + 4 = 17
Probability of getting a white marble = Favorable outcomes/Total outcomes
= 8/17
Therefore, probability of getting a white marble is 8/17
(iii)不是绿色
解决方案：
Number of red marbles = 5
Number of white marbles = 8
Number of green marbles = 4
Total number of marbles = 5 + 8 + 4 = 17
Total number of non-green marbles = 5 + 8 = 13
Probability of getting a non-green marble = Favorable outcomes/Total outcomes
= 13/17
Therefore, probability of getting a non-green marble is 13/17
问题14.如果在袋子中放入21个辅音和5个元音。什么会带来更大的可能性?得到辅音还是元音?找到每个概率?
解决方案：
Number of consonants = 21
Number of vowels = 5
Total number of alphabets = 21 + 5 = 26
Probability of getting a consonant is =Favorable outcomes/Total outcomes
= 21/26
Probability of getting a vowel is = Favorable outcomes/Total outcomes
= 5/26
Therefore, the probability of getting a consonant is greater.
问题15：如果我们班上有15个男孩和5个女孩，则可能性更高?获取属于男孩或女孩的副本。你能给它一个价值吗?
解决方案：
Number of boys = 15
Number of girls = 5
Total number of students = 15 + 5 = 20
Probability of getting a copy of a boy = Favorable outcomes/Total outcomes
= 15/20
= 3/4
Probability of getting a copy of a girl = Favorable outcomes/Total outcomes
= 5/20
= 1/4
Therefore, the probability of getting a copy of a boy is higher.
问题16.如果您有6双白色袜子和3双黑色袜子的集合。您选择不看对的几率是多少
(i)白色?
解决方案：
Number of a pair of white socks = 6
Number of a pair of black socks = 3
Total number pairs of socks = 6 + 3 = 9
Probability of getting a white socks = Favorable outcomes/Total outcomes
= 6/9
= 2/3
Therefore, the probability of white socks is 2/3.
(ii)黑色?
解决方案：
Number of a pair of white socks = 6
Number of a pair of black socks = 3
Total number pairs of socks = 6 + 3 = 9
Probability of getting a black socks = Favorable outcomes/Total outcomes
= 3/9
= 1/3
Therefore, the probability of black socks is 1/3.
问题17.如果您的纺车带有3个绿色扇区，1个蓝色扇区和1个红色扇区。获得绿色部门的可能性是多少?是最大吗?
解决方案：
Number of green sectors = 3
Number of blue sector = 1
Number of red sector = 1
Total number of sectors = 3 + 1 + 1 = 5
Probability of getting a green sector = Favorable outcomes/Total outcomes
= 3/5
Probability of getting a blue sector = Favorable outcomes/Total outcomes
= 1/5
Probability of getting a red sector = Favorable outcomes/Total outcomes
= 1/5
Yes, the probability of getting a green sector is maximum.
问题18.当掷出两个骰子时：
(i)列出总数为奇数的事件的结果。
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)
Outcomes for the event that the total is odd are (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5)
(ii)求出总和为奇数的概率。
解决方案：
Total outcomes = 36
Outcomes for total odd = 18
Probability of getting an event that the total is odd = Favorable outcomes/Total outcomes
= 18/36
= 1/2
Therefore, the probability of getting an odd total is 1/2
(iii)列出事件总数小于5的结果。
解决方案：
Total outcomes = 36
Outcomes of the event that total is less than 5 are: (1, 1), (1,2), (1,3), (2,1), (2,2), (3,1)
(iv)找到总数小于5的概率吗?
解决方案：
Total outcomes = 36
Outcomes for total less than 5 = 6
Probability of getting an event that total is less than 5 = Favorable outcomes/Total outcomes
= 6/36
= 1/6
Therefore, the probability of getting an event that total is less than 5 is 1/6