在以下1到7的每个问题中，描述指定实验的样本空间。
问题1.一枚硬币被扔了三遍。
解决方案：
Suppose if you have a coin in your pocket and you want to play head and tails with the coin. The condition of the game is you should only toss the coin for three times so, when you flip a coin there is an equal chance of getting both head(H) and tail(T) right?
So, there are 2 possibilities and you flipped the coin 3 times which
is 2^3 = 8.
The above discussion says there are 8 possible outcomes when you flipped a coin
3 times, and they are {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}
问题2.掷两次骰子。
解决方案：
When you roll a die there are 6 possible outcomes
So, if you roll the same die for 2 times there are 6*6 = 36 possible outcomes and they 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)}
问题3.一枚硬币被扔了四次。
解决方案：
There are 2 possible outcomes head(H) and tail(T) when you flip a coin.
If you flip the coin for 4 times there will are 2*2*2*2 = 2^4 = 16 possible outcomes, and they are:
{HHHH, THHH, HTHH, HHTH, HHHT, TTTT, HTTT, THTT, TTHT, TTTH, TTHH, HHTT,
THTH, HTHT, THHT, HTTH}
问题4.投掷硬币并掷出骰子。
解决方案：
When you flip a coin there are 2 possible outcomes head(H) and tail(T) when you roll a die there are 6 possible outcomes 1,2,3,4,5,6
So, the possible outcomes will be 2*6 = 12, and they are:
{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
问题5：仅在硬币上显示头像的情况下，才抛硬币，然后掷骰子。
解决方案：
There are 2 possible outcomes head(H) and tail(T) when you flip a coin.
When you roll a die there are 6 possible outcomes 1, 2, 3, 4, 5, 6
So, when you get a head the possible outcomes of a die will be 6.
And there is also a chance of getting a tail i.e. 1 so, the possible outcomes will be 6+1 = 7, and they are:
{H1, H2, H3, H4, H5, H6, T}
问题6。X室中有2个男孩和2个女孩，Y室中有1个男孩和3个女孩。为实验指定样本空间，先选择一个房间，再选择一个人。
解决方案：
Let us take boys as B1, B2 and girls as G1, G2 in room X in the same way let us take boys as B3 and girls as G3, G4, G5 in room Y.
If room X is selected the possible outcome will be {(X,B1), (X,B2), (X,G1), (X,G2)}
If room Y is selected the possible outcome will be {(Y,B3), (Y,G3), (Y,G4), (Y,G5)}
The total sample space will be: {(X,B1), (X,B2), (X,G1), (X,G2), (Y,B3), (Y,G3), (Y,G4), (Y,G5)}
问题7：将一个红色的骰子，一个白色的骰子和一个蓝色的骰子放在袋子中。随机选择一个骰子并滚动，记下其颜色和最上面的数字。描述样本空间。
解决方案：
If we roll the die there are 6 possible outcomes 1, 2, 3, 4, 5, 6 and if we roll the same die for three times the possible outcomes will be 6*3 = 18.
Assume that red colour, white colour and blue colour are denoted as R, W, B respectively.
Then the all 18 possible outcomes(sample space) will be:
{(R,1),(R,2),(R,3),(R,4),(R,5),(R,6),(W,1),(W,2),(W,3),(W,4),(W,5),(W,6) (B,1),(B,2),(B,3),(B,4),(B,5),(B,6)}
问题8：一项实验包括记录有2个孩子的家庭的男孩女孩组成。
(i)如果我们有兴趣了解按出生顺序排列的是男孩还是女孩，那么样本空间是多少?
(ii)如果我们对家庭中的女孩数量感兴趣的话，样本空间是多少?
解决方案：
Assume boy as B and girl as G
i) If it is a boy or girl we have the sample space as {GG, BB, GB, BG}
ii) If it is a girl and if there are 2 girl child’s in the family the sample space is {GG} and if there is one girl child in the family the sample space will be (GB, BG} so, in total we have a sample space as {GG, GB, BG}
问题9.一个盒子包含1个红色和3个相同的白色小球。连续随机抽出两个球，无需替换。编写此实验的样本空间。
解决方案：
Let us assume that R as red ball and W as white ball.
Given in the question that white balls are identical so, if we pick any one of the three white balls is same.
So, the total number of spaces will be (2^2)-1 = 3, and they will be {WW, WR, RW}.
问题10.实验包括抛硬币，如果发生头部抛掷，则第二次抛硬币。如果在第一次投掷时出现尾巴，则将骰子滚动一次。找到样本空间。
解决方案：
There are 2 possible outcomes head(H) and tail(T) when you flip a coin. When you roll a die there are 6 possible outcomes 1, 2, 3, 4, 5, 6
When you get a head(H):
You should flip a coin another time when the sample space will be: {HT, HH}
When you get a tail(T):
You should die a roll where the sample space will be: {(T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}
The total sample space will be: {(HT), (HH), (T1), (T2), (T3), (T4), (T5), (T6)}
问题11.假设从很多中随机选择了3个灯泡。每个灯泡均经过测试，并分为有缺陷(D)或无缺陷(N)。编写此实验的样本空间。
解决方案：
There are two possible outcomes either Defective(D) or Non-defective(N) and there are three bulbs now, the sample space will be 2^3 = 8.
And the possible outcomes will be: {DDD, DDN, DND, NDD, DNN, NDN, NND, NNN}
问题12：扔硬币。如果结果是正面，则抛出死角。如果骰子显示偶数，则再次抛出骰子。实验的样本空间是多少?
解决方案：
There are 2 possible outcomes head(H) and tail(T) when you flip a coin.
When you roll a die there are 6 possible outcomes 1,2,3,4,5,6
When the outcome is a head and die shows odd number the sample space will be:
{(H,1), (H,3), (H,5)}
When the outcome is a head and die shows even number the sample space will be:
Now, we need to roll a die again and the sample space will be of (1*3*6 = 18) and they are:
{(H,2,1), (H,2,2), (H,2,3), (H,2,4), (H,2,5), (H,2,6), (H,4,1), (H,4,2), (H,4,3), (H,2,4), (H, 4,5), (H,4,6), (H,6,1),
(H,6,2), (H,6,3), (H,6,4), (H,6,5), (H,6,6)}
When the outcome is tail: The outcome will be 1 i.e. (T).
The overall sample space will be 22 and they are:
{(H,1), (H,3), (H,5), (H,2,1), (H,2,2), (H,2,3), (H,2,4), (H,2,5), (H,2,6), (H,4,1), (H,4,2), (H,4,3), (H,2,4), (H,4,5),
(H,4,6), (H,6,1), (H,6,2), (H,6,3), (H,6,4), (H,6,5), (H,6,6), (T)}
问题13：数字1、2、3和4分别写在四张纸上。将玻片放入盒中并充分混合。一个人从盒子里抽出两张纸条，一张一张接一张，没有替换。描述实验的样本空间。
解决方案：
The numbers written on the slips are 1,2,3,4. Now if I am picking the first slip the probability will be 4 and I picked it and the box is left with 3 more slips and now, I am picking another slip where probability will be 3.
Therefore, the sample space will be
4*3 = 12 and they are:
{(1,2), (1,3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2), (3,4), (4,1), (4,2), (4,3)}
问题14.实验包括滚动一个骰子，然后如果骰子上的数字为偶数，则将硬币抛一次。如果骰子上的数字是奇数，则将硬币掷两次。编写此实验的样本空间。
解决方案：
There are 2 possible outcomes head(H) and tail(T) when you flip a coin.
When you roll a die there are 6 possible outcomes 1, 2, 3, 4, 5, 6
If the number on the die is even:
The sample space will be 6, and they are: {(2, H),(4,H),(6,H),(2,T),(4,T),(6,T)}
If the number on the die is odd:
We should roll the die twice and the sample space is 12 and they are:
{(1,H,H), (3,H,H), (5,H,H), (1,H,T), (3,H,T), (5,H,T), (1,T,H), (3,T,H), (5,T,H), (1,T,T), (3,T,T), (5,T,T)}
The total sample space will be:
{(2,H), (4,H), (6,H), (2,T), (4,T), (6,T), (1,H,H), (3,H,H), (5,H,H), (1,H,T), (3,H,T), (5,H,T), (1,T,H), (3,T,H), (5,T,H), (1,T,T), (3,T,T), (5,T,T)}
问题15：扔硬币。如果显示尾巴，我们从包含2个红色和3个黑色球的盒子中抽出一个球。如果显示头部，我们将死一个人。找到该实验的样本空间。
解决方案：
There are 2 possible outcomes head(H) and tail(T) when you flip a coin.
Assume R1, R2 as two red balls and B1, B2, B3 as three black balls.
If the coin shows a tail:
The sample space will be 5, and they are: {(TR1), (TR2), (TB1), (TB2), (TB3)}
If the coin shows a head:
We throw a die. The sample space will be 5, and they are {(H,1), (H,2), (H,3), (H,4), (H,5), (H,6)}
The overall sample space will be:
{(T,R1), (T,R2), (T,B1), (T,B2), (T,B3), (H,1), (H,2), (H,3), (H,4), (H,5), (H,6)}
问题16：反复掷骰子，直到掷出六个骰子为止。此实验的样本空间是多少?
解决方案：
When you roll a die there are 6 possible outcomes 1,2,3,4,5,6
When you get 6 on the first throw, the sample space will be: {6}
When you get 6 on the second throw, the sample space will be: {(1,6), (2,6), (3,6), (4,6), (5,6)}
When you get 6 on the third throw, the sample space will be: {(1,1,6),(1,2,6),(1,3,6),……}
The sample space is infinitely defined. This process can go infinite times.