Sample Space

Q.

Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is?

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

Q.

Let $\mathrm{\omega }$ be a complex cube root of unity with $\mathrm{\omega }\ne 1$. A fair die is thrown three times. If $\mathrm{r}1,\mathrm{r}2$ and $\mathrm{r}3$ are the numbers obtained on the die, then the probability that ${\mathrm{\omega }}^{\mathrm{r}1}+{\mathrm{\omega }}^{\mathrm{r}2}+{\mathrm{\omega }}^{\mathrm{r}3}=0$ is

1. $1/18$

2. $1/9$

3. $2/9$

4. $1/36$

Q.

There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?

Q. A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Q. 2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

Q. One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.

Q. A box contains $10$ red marbles, $20$ blue marbles and $30$ green marbles, $5$ marbles are drawn from the box what is the probability that
(i) all will be blue? (ii) atleast one will be green?

Q. In the experiment where we throw two dice, the number of possible outcomes is .

1. 6
2. 12
3. 36
4. 18

Q. If $\omega (\ne 1)$ is a cube root of unity, then
$\left|\begin{array}{ccc}1& 1+i+{\omega }^2& {\omega }^2\\ 1-i& -1& {\omega }^2-1\\ -i& -i+\omega -1& -1\end{array}\right|$ equals

1. 0
2. 1
3. i
4. 

Q. Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.

Q. 15. In how many ways can a batsman can score 20 runs in 6 balls. (A) If he can get runs (0, 1, 2, 3, 4, 5, 6) in 1 ball. (B) lf he can get runs (1, 2, 3, 4, 5, 6) in 1 ball.

Q.

Describe the sample space for the indicated experiment.
A die is thrown two times.

Q.

Tickets numbered from 1 to 12 are mixed up together and then a ticket is withdrawn at random. Find the probability that the ticket has a number which is a multiple of 2 or 3.

Q.

From the employees of a company, 5 persons are selected to represents them in the managing committee of the company. Particulars of five persons are as follows:
$$\begin{array}{cccc}\text{S. No.}& \text{Name}& \text{Sex}& \text{Age in years}\\ 1& \text{Harish}& M& 30\\ 2& \text{Rohan}& M& 33\\ 3& \text{Sheetal}& F& 46\\ 4& \text{Alice}& F& 28\\ 5& \text{Salim}& M& 41\end{array}$$
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over 35 years?

Q. In a random experiment of drawing a card from a well-shuffled pack of 52 cards, let A, B, C & D are the events of drawing an ace, a spade, a heart and a diamond respectively.Show that the events A & B , C& A, A& D are not manually exclusive while the event B & C, C & D, B& D are manually exclusive.Show also that the events A, B, C, D are not exhaustive.

Q. Describe the sample space for the indicated experiment : A coin is tossed three times

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

Q. Let $\omega$ be a complex cube root of unity with $\omega \ne 1$. A fair die is thrown three times. If $r_1,r_{2}and{r}_3$ are the numbers obtained on the die, then the probability that ${\omega }^{r_1}+{\omega }^{r_2}+{\omega }^{r_3}=0,$ is ?

1. $\frac{1}{18}$
2. $\frac{1}{9}$
3. $\frac{2}{9}$
4. $\frac{1}{36}$

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.

Outcome is the set of all possible sample space

1. True

2. False

Q.

How many outcomes are there in the sample space of throwing two dice?

Q. An experiment consists of recording 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 girls in the family?

Q. In a single throw of a die describe the following events:
(i) A = Getting a number less than 7
(ii) B = Getting a number greater than 7
(iii) C = Getting a multiple of 3
(iv) D = Getting a number less than 4
(v) E = Getting an even number greater than 4
(vi) F = Getting a number not less than 3.
Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and $\overline{F}$.

Q. A box contains 2 fifty paise coins, 5 twenty five paise coins and a certain fixed number $n(\ge 2)$ of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these 5 coins is less than one rupee and fifty paise.

1. $\frac{10(n+2)}{{}^{n+5}{C}_7}$
2. $1-\frac{10(n+2)}{{}^{n+7}{C}_5}$
3. $\frac{10(n+2)}{{}^{n+7}{C}_5}$
4. $1-\frac{10(n+2)}{{}^{n+5}{C}_7}$

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

Q. There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?

Q. A(n) is the set of all possible outcomes in a random experiment

1. sample space
2. event
3. favourable outcome

Q. The number of favourable outcomes in an event is always greater than the total number of outcomes.

1. False
2. True

Q. Describe the sample space for the indicated experiment : A coin is tossed four times

Q. Suppose $3$ bulbs are selected at random from a lot. Each bulb is tested and classified as defective $\left(D\right)$ or non-defective $\left(N\right)$. The sample space of this experiment is:

1. $\{DDD,DDN,DND,NDD,DNN,NDN,NND,NNN\}$
2. $\{DDN,DND,NDD,DNN,NDN,NND\}$
3. $\{DNN,NDN,NND,NNN\}$
4. $\{DDD,NNN\}$