Sample Space

Q. If the numbers $1,2,3$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after other, without replacement, then the odds against the number $1$ on the first slip is

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

2. {{P}, {FP}, {F, F, P}, {F, F, F, P}, {F, F, F, F, P} {F, F, F, F, F}}

3. None of these

4. {{P}, {FP}, {F, F, P}, {F, F, F, P}, {F, F, F, F, P}}

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. Arun wants to predict the runs India will score in the next ball. The present score is 100 runs in 25 overs and he wants to predict the score when it is 25 overs and 1 ball. What is the sample set? (India is batting first)

1. {100, 101, 102, 103, 104, 105.......}

2. {101, 102, 103.........}

3. {101, 102, 103, 104, 106}

4. {100, 101, 102, 103, 104, 106}

Q.

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

___

Q.

Outcome is the set of all possible sample space

1. True

2. False

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

Q. If two different numbers are taken from the set {0, 1, 2, 3, .... 10}, then the probability that their sum as well as absolute difference are both multiple of 4, is ?

1. $\frac{6}{55}$
2. $\frac{12}{55}$
3. $\frac{14}{45}$
4. $\frac{7}{55}$

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. $\frac{127}{216}$

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

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

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

Q. Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even is ?

1. $\frac{1}{2}$
2. $\frac{36}{55}$
3. $\frac{6}{11}$
4. $\frac{5}{11}$