Union and Intersection of Events

Q.

The probability that a leap year selected at random will contain either $53$Thursday or $53$Friday is

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

1. $\frac{3}{7}$

2. $\frac{2}{7}$

3. $\frac{5}{7}$

4. $\frac{1}{7}$

Q.

Let $E1,E2,E3$ be three arbitrary of a sample space $S$. Consider the following statements which of the following statements are correct.

1. $P\left(\text{only one of them occurs}\right)=P\left(E1E2E3+E1E2E3+E1E2E3\right)$

2. $P\left(\text{none of them occurs}\right)=P\left(E1+E2+E3\right)$

3. $P\left(\text{at least one of them occurs}\right)=P\left(E1+E2+E3\right)$

4. $P\left(\text{all the three occurs}\right)=P\left(E1+E2+E3\right)$

Q.

Represent ((A’$\cup$ B’) – A )’ using a Venn diagram

Q. If $A=\{2,3,5\},B=\{2,5,6\}$ then $(A-B)\times (A\cap B)$ is

1. $\{(3,2),(3,5)\}$
2. $\{(3,2),(3,3),(3,5)\}$
3. $\{(3,2),(3,5),(3,6)\}$
4. None of these

Q. The following table gives the height of trees

Height	Less than $7$	Less than $14$	Less than $21$	Less than $28$	Less than $35$	Less than $42$	Less than $49$	Less than $56$
No. of trees	$25$	$45$	$95$	$140$	$235$	$275$	$320$	$360$

Draw "less than" ogive and "more than" ogive

Q. The shaded portion in the figure represents $A\cap B$.

1. False
2. True

Q. The shaded region in the figure represents $(A\cup B{)}^{\prime }.$

1. False
2. True

Q. $\mathrm{For}\mathrm{any}\mathrm{event}A,\mathrm{The}\mathrm{event}A\cup \overline{A}\mathrm{will}\mathrm{contain}\mathrm{all}\mathrm{the}\mathrm{elements}\mathrm{of}\mathrm{the}\mathrm{sample}\mathrm{space}$

1. True
2. False

Q.

If A = {Factors of 4} and B = {Factors of 5}, then $A\cap B$ is __________ .

1. {1, 2}

2. {1, 2, 4, 5}

3. {2, 4, 6}

4. {1}

Q. Label the indicated parts.

1. $A\cap (B\cup C)$
2. $(B\cap C)-A$
3. $A\cup (B\cap C)$
4. $(B\cup C)-A$

Q. The probability of happening an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of happening neither A nor B is

1. 0.2
2. 0.21
3. 0.6
4. None of these

Q. Probability of a fraudster being caught is $\frac{1}{2}$ and committing a fraud is $\frac{3}{5}$. What is his chance of not going to jail?

1. 40%
2. 35%
3. 70%
4. 50%