问题13.一个盒子包含1个红色和3个黑色的球。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：
The box contains 1 red and 3 black balls and two balls are drawn without replacement , so the sample space associated with this event can be given as:
S = { (R,B1), (R,B2), (R,B3), (B1,R), (B1,B2), (B1,B2), (B2,R), (B2,B1), (B2,B3), (B3,R), (B3,B1), (B3,B2) }
问题14：掷出一对骰子。如果结果加倍，则投掷一枚硬币。确定与实验相关的基本事件的总数。
解决方案：
When a pair of dice is rolled, then there are in total 6 x 6 = 36 possible outcomes.
The term doublet refers to the event when the pair of dice after rolling has outcomes as (1,1), (2,2), (3,3), (4,4), (5,5), (6,6), when a double is obtained then again the coin is tossed and we have outcome as either head (H) or tail (T).
Therefore, total number of elementary events = (36-6) + 6 x 2 = 30 + 12 = 42.
问题15：一枚硬币被扔了两次。如果第二次抽奖导致压头，则掷骰子。编写此实验的样本空间。
解决方案：
When two coins are tossed, then we have four possible outcomes as HH, HT, TH, TT. Now for those cases where in second draw head comes, we throw a die, then the sample space is written as:
S’ = { (HH,1), (HH,2), (HH,3), (HH,4), (HH,5), (HH,6),
(TH,1), (TH,2), (TH,3), (TH,4), (TH,5), (TH,6) }
Therefore, sample space for the entire experiment can be written as:
S = { (HT), (TT). (HH,1), (HH,2), (HH,3), (HH,4), (HH,5), (HH,6), (TH,1), (TH,2), (TH,3), (TH,4), (TH,5), (TH,6) }
问题16.一个袋子包含4个相同的红色球和3个相同的黑色球。实验包括画一个球，然后将其放入袋子，然后再画一个球。实验的可能结果是什么?
解决方案：
Since, we have identical balls inside the bag, we can denote each red ball using a common notation as R and similarly each black ball can be denoted using symbol B.
So, after first draw the sample space will be S1 = {R,B}, the ball is again put back in the bag, so again for second draw sample space will be S2 = {R,B}.
Hence, sample space for the entire event is S = { RR, RB, BR, BB }
问题17.在随机抽样中，从很多中选择了三个项目。每个项目均经过测试，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：
Three items stored in the lot can be: (a) all defective (b) all non-defective (c) a mixture of both defective and non-defective items.
Therefore, the possible sample space associated with this experiment can be given as:
S = {DDD, DDN, DND, NDD, NNN, NND. NDN, DNN }
问题18：一个实验由有两个孩子的家庭的男孩女孩组成。
(i)如果我们有兴趣按出生顺序了解是男孩还是女孩，那么样本空间是多少?
(ii)如果我们对一个家庭中男孩的数量感兴趣的话，样本空间是多少?
解决方案：
According to the question, if a family consists of two children then sample space can be given as:
(i) S = { (B1,B2), (B1,G2), (G1,B2), (G1,G2) }, the number represents the first and second child.
(ii) Since, there can be at most two children, there are three possibilities:
a) the family has 0 boys
b) the family has 1 boy
c) the family has 2 boys
Hence, the sample space S = {0,1,2}
问题19.有三个彩色骰子，分别是红色，白色和黑色。这些骰子放在袋子里。从袋子中随机抽出一个骰子并滚动，注意其颜色和面上的数字描述了实验的样品空间。
解决方案：
If we pick red colored dice and draw its sample space can be given as:
S1 = { (R,1), (R,2), (R,3), (R,4), (R,5), (R,6) }
similarly, If we pick red colored dice and draw its sample space can be given as:
S2 = { (B,1), (B,2), (B,3), (B,4), (B,5), (B,6) }
similarly, If we pick white colored dice and draw its sample space can be given as:
S3 = { (W,1), (W,2), (W,3), (W.4), (W,5), (W,6) }
Hence, sample space for the entire experiment = S1 U S2 U S3
= { (R,1), (R,2), (R,3), (R,4), (R,5), (R,6),
(B,1), (B,2), (B,3), (B,4), (B,5), (B,6),
(W,1), (W,2), (W,3), (W.4), (W,5), (W,6) }
问题20.在房间P中有2个男孩和2个女孩，在房间Q中有1个男孩3个女孩。写出用于实验的样本空间，先选择一个房间，然后选择一个人。
解决方案：
There are in total 2 rooms.
| Rooms | P | Q |
| Boys | 2 | 1 |
| Girls | 2 | 3 |
We can select a room in two ways: either P or Q, also selecting a person from a room can be done in from P in 4 ways. Similarly, from Q it can be done in 4 ways.
Therefore, sample space for this experiment can be written as:
S = { (P,B1), (P,B2), (P,G1), (P,G2),
(Q,B3), (Q,G3), (Q,G4), (Q,G5) }
问题21.一个袋子包含一个白色和一个红色的球。从袋子里抽出一个球。如果拉出的球是白色的，则将其放回袋子中，然后再次拉出一个球。否则，将掷出骰子。编写此实验的样本空间。
解决方案：
Out of two balls, if we draw a ball, it will be either red (R) or white (W).
When a white ball is drawn, it is replaced and then again a ball is drawn, therefore sample space
S1 = { (W,W), (W,R) }
Also, if a red ball is drawn then a die is rolled, therefore sample space
S2 = { (R,1), (R,2), (R,3), (R,4), (R,5), (R,6) }
Hence, sample space for the entire experiment, S = S1 U S2
S = { (W,W), (W,R), (R,1), (R,2), (R,3), (R,4), (R,5), (R,6) }
问题22.一个盒子包含1个白色和3个相同的黑色球。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：
Since, we have identical black balls inside the box, we can denote each black ball using a common notation as B. Now, sample space for drawing two balls without replacement can be written as:
S = { (W,B), (B,W), (B,B) }
问题23：一个实验包括滚动一个骰子，然后如果骰子上的数字是偶数，则将硬币扔一次。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：
Sample space for throwing a die:
S1 = { 1, 2, 3, 4, 5, 6 }
If the even number turns up on the dice, then a coin is tossed, so
S2 = { (2,H), (2,T), (4,H), (4,T), (6,H), (6,T) }
whereas when an odd number turns up on the dice, then a coin is tossed two times, so
S3 = { (1,HH), (1,HT), (1,TH), (1,TT), (3,HH), (3,HT),(3,TH), (3,TH), (5,HH), (5,HT), (5,TH), (5,TT) }
Therefore, sample space for the entire experiment, S = S2 U S3
S = { (2,H), (2,T), (4,H), (4,T), (6,H), (6,T),
(1,HH), (1,HT), (1,TH), (1,TT), (3,HH), (3,HT),
(3,TH), (3,TH), (5,HH), (5,HT), (5,TH), (5,TT) }
问题24.反复投掷骰子，直到出现6个骰子为止。此实验的样本空间是多少。
解决方案：
According to the question the die keeps on rolling till we not get a six. So, the sample space can be written as:
S = { 6, (1,6), (2,6), (3,6), (4,6), (5,6), (1,1,6), (1,2,6), (1,3,6), (1,4,6), (1,5,6), (2,1,6), (2,2,6), (2,3,6), ……….. }