Sample Space

Q. The probability that two randomly selected subsets of the set $\{1,2,3,4,5\}$ have exactly two elements in their intersection, is

1. $\frac{135}{2^9}$
2. $\frac{65}{2^8}$
3. $\frac{65}{2^7}$
4. $\frac{35}{2^7}$

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

1. False
2. True

Q. A random variable $X$ has the following probability distribution:
$$\begin{array}{cccccc}X& 1& 2& 3& 4& 5\\ P\left(X\right)& K^2& 2K& K& 2K& 5K^2\end{array}$$
Then $P(X>2)$ is equal to:

1. $\frac{7}{12}$
2. $\frac{1}{6}$
3. $\frac{23}{36}$
4. $\frac{1}{36}$

Q. A glass contains 4 red balls, 3 white balls, 2 yellow balls, 20 black balls. We are drawing one ball at random from the jar. The number of elements in the set of sample space of the above experiment if the balls of same color are not identical is $\underset{–}{}$___

Q. A glass contains 4 red balls, 3 white balls, 2 yellow balls, 20 black balls. We are drawing one ball at random from the jar. The number of elements in the set of sample space of the above experiment if the balls of same color are not identical is $\underset{–}{}$___

Q. The probability that length of a randomly selected chord of a circle lies between $\frac{1}{2}$ and $\frac{3}{2}$ of its radius is
(correct answer + 1, wrong answer - 0.25)

1. $\frac{9}{16}$
2. $\frac{1}{2}$
3. $\frac{2}{3}$
4. $\frac{4}{9}$

Q. The probability that a teacher will give an unannounced test during any class meeting is $\frac{1}{5}$.If a student is absent twice, the probability that he will miss atleast one test, is

1. $\frac{7}{25}$
2. $\frac{9}{25}$
3. $\frac{16}{25}$
4. $\frac{24}{25}$

Q. How many outcomes are there in the sample space of an event defined as "throwing two dice and a coin together"

Q. Two numbers b and c are chosen at random (with replacement from the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9). The probability that $x^2+bx+c>0$ for all $x\in R$ is

1. $\frac{17}{123}$
2. $\frac{82}{125}$
3. $\frac{45}{143}$
4. $\frac{32}{81}$

Q.

Rohan attends a test with multiple choice questions with no negative marking. There were fifty questions and each question had four marks for answering right. What is the sample space of marks that Rohan could score?

1. {0, 1, 2, 3, ..... 50}

2. {0, 4, 8, 12, ..... 200}

3. {0, 1, 2, 3, ..... 200}

4. {0, 4, 8, 12, ..... 50}

Q. Which of the following is the sample space for the following experiment?
We toss a coin until we see two consecutive tails. We record the total number of coin tosses.

1. Set of positive integers
2. Set of natural numbers
3. None of the above
4. Set of natural number greater than or equal to 2

Q.

Four fair dice $D_1,D_2,D_{3}and{D}_4$ each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1,D_{2}and{D}_3$, is ?

1. $\frac{91}{216}$

2. $\frac{108}{216}$

3. $\frac{125}{216}$

4. $\frac{127}{216}$

Q. Two unbiased dice are rolled. The number of elements in the sample space of the above experiment will be $\underset{–}{}$___

Q. It is impossible that, a sure event and an impossible event takes place together in an experiment.

1. False
2. True

Q. For the random experiment of removing two balls from a bag containing 4 red, 1 green and 3 blue balls, which of the following ordered pairs is not a sample point?
(Here 'R', 'G', 'B' denote red, green and blue ball respectively.)

1. (R, B)
2. (B, B)
3. (G, R)
4. (G, G)

Q. One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

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

Q.

Papu takes a test and he is very 'determined' about passing the test. He will not give up until he passes the test. How would the sample space of results look like if p stands for pass and F stands for fail, given that he can take the test atmost five times and no test after passing?

1. {{P}, {FP}, {F, F, P}, {F, F, F, P}, {F, F, F, F, P}}

2. {{F}, {PF}, {P, P, F}, {P, P, P, F}}

3. {{P}, {FP}, {F, F, P}, {F, F, F, P}, {F, F, F, F, P} {F, F, F, F, F}}

4. None of these