Sample Space

Q.

A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?

Q.

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

Q.

Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting all the four cards of the same number.

Q. To promote making of toilets for women, an organisation tried to generate awarness through (i) house calls, (ii) letters, and (iii) announcements. The cost for each mode per attempt is given below:
(i) ₹50 (ii) ₹20 (iii) ₹40

The number of attempts made in three villages X, Y and Z are given below:
(i) (ii) (iii)
X 400 300 100
Y 300 250 75
Z 500 400 150

Find the total cost incurred by the organisation for three villages separately, using matrices.

Q.

Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5.

Q. The total number of elements in the sample space for the experiment where a coin is tossed and a die is thrown is:

1. $6$
2. $12$
3. $36$
4. $4$

Q. Consider the experiment in which a coin is tossed repeatedly until a head comes up. Then the sample space is:

1. $S=\{H,TH,TTH,HTTH,TTTTH,\cdots \}$
2. $S=\{H,TH,THH,TTTH,THHTH,\cdots \}$
3. $S=\{H,TH,TTH,TTTH,TTTTH,\cdots \}$
4. $S=\{T,TH,TTH,TTTH,TTTTH,\cdots \}$

Q.

2 boys and 2 girls are in room P and 1 boy 3 girls are in room Q. Write the same space for the experiment in Which a room is selected and then a person

Q. Box $1$ contains three cards bearing numbers $1,2,3;$ box $2$ contains five cards bearing numbers $1,2,3,4,5;$ and box $3$ contains seven cards bearing numbers $1,2,3,4,5,6,7.$ A card is drawn from each of the boxes. Let $x_i$ be the number on the card drawn from the $i^{th}$ box, $i=1,2,3.$

The probability that $x_1,x_2,x_3$ are in an arithmetic progression, is

1. $\frac{9}{105}$
2. $\frac{10}{105}$
3. $\frac{11}{105}$
4. $\frac{7}{105}$

Q. If from a group of 2 boys and 2 girls, two persons are selected randomly then how many elements will be there in the sample space?

1. 
   2
2. 
   4
3. 
   6
4. 
   8

Q. In a group 14 males and 6 females, 8 and 3 of the males and females respectively are aged above 40 years. The probability that a person selected at random from the group is aged above 40 years, given that the slelected person is a female, is

1. $\frac{2}{7}$
2. $\frac{1}{2}$
3. $\frac{1}{4}$
4. $\frac{5}{6}$

Q.

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

Q.

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done, is equal to?

1. $3$

2. $36$

3. $66$

4. $108$

Q.

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.

Q.

The number of ways in which score of 11 can be made from a throw by three persons is throwing a single die once, is

(a) 45 (b) 18

(c) 27 (d) 68

Q.

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

Q. Four tickets marked $00,01,10,11$ respectively are placed in a bag. A ticket is drawn at random five times, being replaced each time. The probability that the sum of the number on tickets thus drawn is $23,$ is

1. $\frac{41}{1024}$
2. $\frac{25}{256}$
3. $\frac{25}{178}$
4. $\frac{21}{256}$

Q.

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

Q. find the number of ways of selecting 9 balls from 6 red balls, 5 white balls , 5 blueballs if each selections consists of 3 balls of each colour.

Q. The sample space of the experiment: 'A coin is tossed until two consecutive tails appeared and the total number of coin tosses are recorded' is

1. positive integers
2. natural numbers
3. natural numbers $\ge 2$

Q. A person plays a game of tossing a coin thrice. For each head, he is given Rs $2$ by the organiser of the game and for each tail, he has to give Rs $1.50$ to the organiser. Let $X$ denotes the amount gained or lost by the person. Then range of $X$ is:
(Where minus sign shows the loss to the player and positive sign shows gain to the player)

1. $\{-1\}$
2. $\{-1,2.5\}$
3. $\{-4.5,-1,2.5\}$
4. $\{-4.5,-1,2.5,6\}$

Q.

A fair coin and an unbiased die are tossed. LEt A be he event 'head appears on the coin' and B be the events '3 be the events '3 on the die', Cheek whether A and B are independent events or not.

Q. Let there are $8$ cards numbered $1$ to $8,$ even numbered card is red coloured and odd numbered card is black coloured.
A card is selected at random,
Consider the following events:
$A:$ The selected card is red and the number on the card is divisible by $5.$
$B:$ The selected card is black and the number on the card is divisible by $7$
$C:$ The selected card is red and the number on the card is divisible by $4$
$D:$ The selected card is black and the number on the card is divisible by $3.$
Then which of the following statement(s) is are correct ?

1. $A$ is impossible event.
2. $B$ and $C$ are simple events.
3. $B$ and $D$ are simple events.
4. $C$ is compound event.

Q.

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.

Q.

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

Q.

If S is the sample space associated with a random experiment. Then a real valued function which assign to each element of S, a unique real number is called a …...

1. Random variable

2. Real numbers

3. Random experiment

4. Non-negative integers

Q.

The number of different sums can be formed with the following coins a rupee a fifty paise a twenty five paise a ten paise a five paise?

Q. Find the probability that the 3N’s come consecutive in the arrangement of the letters of the word “CONSTANTINOPLE”.

1. $\frac{3}{91}$
2. $\frac{2}{91}$
3. $\frac{4}{91}$
4. $\frac{2}{91}$

Q.

What is the number of ways of choosing 4cards from a bag of 52 playing cards ? In how many of these :

1) 4 cards are of the same suite

2) 4 cards belong to 4 different suites

3) 4 cards are face cards

4) two are red cards and two are black cards

Q.

There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.