Question 1: A Coin is tossed once. Write its sample space.

Answer:

When a coin is tossed, there are two possibilities. It could either turn up Head (H) or Tail (T).

Hence the sample space will be

Question 2: If a coin is tossed two times, describe the sample space associated to this experiment.

Answer:

Given: If Coin is tossed twice times. In each toss there can be two outcomes. It could either turn up Head (H) or Tail (T).

We know that, the coins are tossed two times, and then the total number of possible outcomes is

Hence the sample space will be

Question 3: If a coin is tossed three times (or three coins are tossed together), then describe the sample
space for this experiment.

Answer:

Given: If a coin is tossed three times.

We know that, the coins are tossed three times, and then the total number of possible outcomes is

Hence the sample space will be

Question 4: Write the sample space for the experiment of tossing a coin four times.

Answer:

When a coin is tossed, there are two possibilities. It could either turn up Head (H) or Tail (T).

We know that, the coins are tossed four times, and then the total number of possible outcomes is

Hence the sample space will be

Question 5: Two dice are thrown. Describe the sample space of this experiment.

Answer:

When a dice is rolled, there are six possibilities. It could either turn up  

We know that, when two dice are rolled , and then the total number of possible outcomes is

Hence the sample space will be

Question 6: What is the total number of elementary events associated to the random experiment of
throwing three dice together?

Answer:

Given: Three dice is rolled together.

We know that, three dice are thrown together.

When a dice is rolled, there are six possibilities. It could either turn up  

So, the total numbers of elementary event on throwing three dice are

Therefore the total number of elementary events are

Question 7: A coin is tossed and then a die is thrown. Describe the sample space for this experiment.

Answer:

Given: A coin is tossed and then a die is thrown.

We know that, the coin is tossed and die is thrown.

When a coin is tossed, there are two possibilities. It could either turn up Head (H) or Tail (T).

When a dice is rolled, there are six possibilities. It could either turn up  

Therefore, The total number of Sample space together is

Hence the sample space will be

Question 8: A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe
the sample space for this experiment.

Answer:

Given: A coin is tossed and then a die is rolled only in case a head is shown on the coin.

When a coin is tossed, there are two possibilities. It could either turn up Head (H) or Tail (T).

When a dice is rolled, there are six possibilities. It could either turn up  

Hence the sample space will be

Question 9: A coin is tossed twice. If the second throw results in a tail, a die is thrown. Describe the sample space for this experiment.

Answer:

Given: A coin is tossed twice. If the second throw results in a tail, a die is thrown.

When a coin tossed twice, then sample spaces for only coin will be:

Now if the second throw results in a tail, a die is thrown. Therefore when We get dice is rolled.

When a dice is rolled, there are six possibilities. It could either turn up  

Hence the sample space will be

Question 10: An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.

Answer:

In the given experiment, coin is tossed and if the outcome is tail then, die will be rolled.

When a coin is tossed, there are two possibilities. It could either turn up Head (H) or Tail (T).

When a dice is rolled, there are six possibilities. It could either turn up  

If the outcome for the coin is tail then sample space is

If the outcome is head then the sample space is

Hence the sample space will be

Question 11: A coin is tossed. If it shows tail we draw a Ball from a box which contains 2 red 3 black balls; if it shows head, we throw a die. Find the sample space of this experiment.

Answer:

When a coin is tossed, there are two possibilities. It could either turn up Head (H) or Tail (T).

Let the two red balls be R1 and R2 and the three black balls be B1, B2 and B3

According to question, If tail turned up, the a ball is drawn from a box.

So, Sample for This experiment

Now, If Head is turned up, then die is rolled.

When a dice is rolled, there are six possibilities. It could either turn up  

So, Sample space for this experiment

Hence the sample space will be

Question 12: A coin is tossed repeatedly until a tail comes up for the first time. Write the sample space for this experiment.

Answer:

Given: A coin is tossed repeatedly until Tail comes up for the first time.

In the given Experiment, a coin is tossed and if the outcome is tail the experiment is over.

And, if the outcome is Head then the coin is tossed again.

In the second toss also if the outcome is tail then experiment is over, otherwise coin is tossed again.

This process continues indefinitely

Hence the sample space will be

Question 13: A box contains 1 red and 3 black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Answer:

Note: You cannot assume that the balls are identical.

Let us denote the red ball as R and the three black balls as B1, B2, and B3.

Hence the sample space will be

Question 14: A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Determine the total number of elementary events associated to this experiment.

Answer:

Given a pair of dice is rolled. If the outcome is a doublet, a coin is tossed.

A pair of dice is rolled,  Then, No. of elementary events are

Now, If outcomes is doublet means then a coin is tossed.

If coin is tossed then no. of sample spaces is

So, The total no. of elementary events including doublet

Thus, The Total number of elementary events are

Hence, events will occur for this experiments.

Question 15: A coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this experiment.

Answer:

A coin is tossed twice , So the outcomes are

Now, If the second drawn result is head , the a die is rolled.

Then the elementary events is

Hence the sample space will be

Question 16: A bag contains 4 identical red balls and 3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment?

Answer:

Given a bag contains 4 identical red balls and 3 identical black balls.

Let us Assume Red

Let us Assume Black

Now, A ball is drawn in first attempt, So elementary events is 

And, The ball will put into the bag and draw again, then elementary events are 

Thus, The total sample space associated is

Question 17: In a random sampling three items are selected from a lot. Each item is tested and classified as defective (D) or non-defective (N). write the sample space of this experiment.

Answer:

In the random sampling , three items are selected so it could be

(a) All defective (D)

(b) All non-defective(N)

(c) Combination of both defective and non defective  We have 2 category (N and D) and we have three condition

So, The number of sample is

Sample space associated with this experiment is 

Question 18: An experiment consists of boy-girl composition of families with 2 children.

(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

(ii) What is the sample space if we are interested in the number of boys  in a family?

Answer:

(i) Here, The family has 2 children

Let us Assume Boy = B  Let us Assume Girl = G

So, The number of sample spaces for 2 children is

Sample space are,

Where , number 1 and 2 are represent elder and younger.

(ii) Here, The family has 2 children, So the possibility of boys in a family is:

(a) No boys only girl

(b) One boy and one girl

(c) Two boys only

So, The Sample space for the given condition is: 

Question 19: There are three colored dice of red, white and black color. These dice are placed in a bag. One die is drawn at random from the bag and rolled, its color and the number on its uppermost face is noted. Describe the sample space for this experiment.

Answer:

When a dice is rolled, there are six possibilities. It could either turn up  

Let us Assume Red = R      White = W     Black = B

According to question,  Dice is selected , then rolled its color and number is noted.

Firstly, selected Red Dice then, Possible samples are: 

Then, White Dice will be selected , Possible samples are: 

Lastly, Black Dice will be selected and rolled, Possible samples are:

Thus, The total sample for the given experiment is

Question 20: 2 boys and 2 girls are in room P and 1 boy 3 girls are in room Q. Write the sample space for
the experiment in which a room is selected and then a person.

Answer:

Let us denote two boys and girls in room as and respectively.

Let us denote 1 boy and 3 girls in room as and respectively.

Sample spaces for room P are

Sample spaces for room Q are 

Now, The total sample spaces for the given experiment: 

Question 21: A bag contains one white and one red ball. A ball is drawn from the bag. If the ball drawn is white it is replaced in the bag and again a ball is drawn. Otherwise, a dice is tossed. Write the sample space for this experiment.

Answer:

There is 1 white ball , 1 red ball in a bag.

Let us denote White ball with W and Red Ball with R.

When one ball is drawn, it may be a White or Red.

So, The sample space of drawing on white ball with replacement 

Again, If red ball is drawn , a dice is rolled

So, The sample space for red ball with dice 

Thus, The required sample space for the experiment is: 

Question 22: A box contains 1 white and 3 identical black balls. Two balls are drawn at random in succession without replacement. write the sample space for this experiment.

Answer:

Let R stands for red ball and W stands for white ball.

Then required sample space 

Question 23: An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

Answer:

A dice has 6 faces that are numbered from 1 to 6.

And, we know, 2, 4, 6 are even numbers and 1, 3, 5 are odd numbers.

Now, A coin has two face, Head(H) and Tail(T)

Therefore the total sample spaces by combining both experiments is

Question 24: A die is thrown repeatedly until a six comes up. What is the sample space for this experiment

Answer:

The die is thrown repeatedly until a six comes up.

It means  Since, 6 may come upon the first throw , second throw , third throw and so on until is obtained.

So, This process will continues indefinitely, then the sample space will be: