**Question 1 **

**Write the sample space when a coin is tossed thrice.**

**Sol:**

We all know that an unbiased coin a head (H) & a tail (T)

According to the question, when a coin tossed thrice, then possible outcomes =

Sample space = { TTT, HHH, HHT, THH, THT, HTH, HTT, TTH, }

**Question 2 **

**Write the sample space when a dice is rolled twice.**

**Sol:**

Possible outcomes when a die is rolled: 3, 6,4,5 &1, 2

If the die is thrown twice, the sample space = {(x,y):x,y = 1,2,3,4,5,6}

Total number of elements in the sample space =

Sample space = { (1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (5,1) , (5,2) ,( 5,3) , (5,4) , (5,5), (5,6) , (3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6) , (4,1) , (4,2) , (4,3) , (4,4) , (4,5) ,(4,6) , (2,1) , (2,2) , (2,3) , (2,4) ,(2,5) , (2,6) , (6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,6) }

**Question 3**

**Write the sample space when a coin is tossed four times.**

**Sol:**

We all know that an unbiased coin has a head (H) & a tail (T)

According to the question, a coin is tossed 4 times, possible outcomes are =

Sample space = {TTTT, TTTH ,TTHT ,TTHH , THTT ,THTH ,THHT ,THHH ,HTTT ,HTTH , HTHT , HTHH , HHTT ,HHTH , HHHT ,HHHH }

**Question 4**

**Find the sample space of a coin and a die are tossed together.**

**Sol:**

We all know that an unbiased coin has a head (H) & a tail (T)

Possible outcomes when a die is thrown: 1, 2,3,4,5 and 6

Thus, sample space of a coin and a die when thrown together

S = {T6 , T5 , T4 , T3 ,T2 , T1 , H6 , H5 , H4 ,H3 ,H2 ,H1 }

**Question 5 **

**Find the sample space when a die is rolled and a coin is tossed only if in case there is head in the coin.**

**Sol:**

We all know that a unbiased coin has a head (H) and a tail (T)

Possible outcomes when a die is thrown: 1, 2,3,4,5 and 6

Thus, sample space of a coin and a die when thrown together

S = { T , H6 , H5 , H4 ,H3 ,H2 ,H1 }

**Question 6**

**Room x is having 2 girls and 2 boys while Room y is having 3 girls and 1 boy. Determine the sample space where a person gets a room.**

**Sol:**

Let us consider 2 girls and 2 boys in room no. x be G_{1},G_{2} & B_{1},B_{2 }.

Also, 3 girls and 1 boy in room no. y be G_{3},G_{4} & G_{5},B_{3 }.

Sample space of the above mentioned problem is = { XG_{1},XG_{2, }XG_{3},XG_{4},XG_{5}, XB_{1},XB_{2., }XB_{3}}

**Question 7**

**A bag contains dies of several colors such as red, white and blue. Dies are selected as random and rolled and the colour and the number in it’s uppermost face is noted down. Determine the sample space.**

**Sol:**

Possible outcomes when a die is thrown: 1, 2,3,4,5 and 6.

Let us consider red, white and blue coloured dices be R , W and B respectively.

According to the question, sample space when a die is rolled = { R6 , R5 , R4 , R3 , R2 , R1 , W6 , W5 , W4 , W3 , W2 , W1 , B6 , B5 , B4 , B3 , B2 , B1 }

**Question 8 **

**An experimental setup consists of a family consisting a boy and a girl with 2 children. **

**(i) Determine the sample space if the person conducting the experiment is interested in knowing whether it is a boy or a girl according to the order of their birth. **

**(ii) Determine the sample space if the person conducting the experiment is interested in knowing the number of girls in the family?**

**Sol:**

(i) Sample space depending the order of birth of a boy or a girl = { BB , BG , GB , GG }

(ii) According to the question, it is said that a family can have only two children . it can either be a boy and a girl , both of them are girls or both of them are boys.

Sample space = { 2,1,0}

**Question 9**

**A experimental setup consists of a box containing 1 red ball and 3 identical white balls. At a time 2 balls are drawn at random in succession without replacement. Find the sample space of the experimental setup.**

**Sol:**

According to the question it is given that the experimental setup contains a box containing a red ball and three identical white balls.

Sample space of the event of drawing 2 balls at random in succession without replacement is = {WW, WR, RW}

**Question 10**

**An experimental setup consists of tossing up of a coin in the air and if head comes up it is tossed again. If a tail occurs in the first event then a die is rolled only once. Find the sample space of the experiment.**

**Sol:**

We all know that an unbiased coin has a head (H) & a tail (T)

Possible outcomes when a die is thrown: 1, 2,3,4,5 and 6

Sample space of the experimental setup = { T6 , T5 , T4 , T3 , T2 , T1 , HT , HH }

**Question 11**

**3 bulbs are selected at a random from a bag of bulbs. Depending upon several tests each bulb is termed as defective or non-defective . Determine the sample space of this series of events.**

**Sol:**

According to the question, it is given that 3 bulbs are selected at a random from a bag of bulbs. Depending upon the series of tests each bulb is termed as either non defective or defective.

Sample space of the series of events = { NNN ,NND ,NDN ,NDD , DNN , DND , DDN , DDD}

**Question 12**

**An experiment consists of tossing a coin. During the conduction of the experiment if head comes up then a die is thrown instantly , if there is any even number on the die then it is thrown again . determine the sample space of the experiment.**

**Sol:**

We all know that an unbiased coin has a head (H) & a tail (T)

Possible outcomes when a die is thrown: 1, 2,3,4,5 and 6

Sample space of the experiment = { H66 , H65 , H64 , H63 , H62 , H61 , H46 , H45 , H44 , H42 , H41 , H26 , H25 , H24 , H23 , H22 H21 , H5 , H3 , H1 , T }

**Question 13**

**A box containing 4 slips of paper written 1,2,3 and 4 separately. They are then mixed thoroughly and drawn one at a time twice without replacement. Determine the sample space of the experiment**

**Sol:**

If 3 appears on the first slip of paper , then the possibilities that the numbers appearing in the next slip of paper will be 1,2 and 4. If 4 appears on the first slip of paper , then the possibilities that the numbers appearing in the next slip of paper will be 1,2 and 3.

Sample space of the experiment = { (4,1) , (4,2) , (4,3) , (3,1) , (3,2) , (3,4) , (2,1) , (2,3) , (2,4) , (1,2) , (1,3) , (1,4) }

**Question 14 **

**An experiment consists of rolling a die then tossing a coin if any even number comes up while rolling the die. Also it was noted that if any odd number comes up the coin is tossed twice. Determine the sample space of the experiment.**

**Sol:**

We all know that an unbiased coin has a head (H) & a tail (T)

Possible outcomes when a die is thrown: 1, 2,3,4,5 and 6

sample space of the conducted experiment = { 5TT , 5TH , 5HT , 5HH ,3TT , 3TH , 3HT , 3HH , 1TT , 1TH ,1HT , 1HH , 6T , 6H , 4T , 4H , 2T , 2H }

**Question 15**

**A coin is tossed if tail comes up a ball is drawn from a box containing 3 black balls and 2 red balls . A die is thrown is head comes up. Determine the sample space of the experiment.**

**Sol:**

According to the question, it is given that a box contains 2 red and 3 black balls and they are named as R_{1},R_{2} and B_{1},B_{2},B_{3}

Sample space of the experiment = { H6 , H5 , H4 , H3 , H1 , TB_{3} , TB_{2 ,}TB_{1} , TR_{2 , }TR _{1}}

**Question 16**

**A die is rolled continuously unless and until a six shows up. Determine the sample space for this experiment.**

**Sol:**

Possible outcomes when a die is thrown: 1, 2,3,4,5 and 6

In this experiment 6 might come up in the 1^{st} throw, 2^{nd} throw, 3^{rd} throw and so on …….

Therefore , the sample space of the experiment = { 6 , (1,6) , (2,6) , (3,6) , (4,6) , (5,6) , ( 1,1,6) , (1,2,6) ……… (1,5,6) , (2,1,6) , (2,2,6) ……………. (2,5,6) ………(5,1,6) , (5,2,6) }