Complement of a Set

Q. If $A$ and $B$ are two events such that $P\left(A\right)=\frac{3}{4}$ and $P\left(B\right)=\frac{5}{8}$, then

1. $P(A\cup B)\ge \frac{3}{4}$
2. $P(A^{\prime }\cup B)\ge \frac{1}{4}$
3. $\frac{3}{8}\le P(A\cup B)\le \frac{5}{8}$
4. $\frac{3}{8}\le P(A\cap B)\le \frac{5}{8}$

Q.

If two events $P\left(AUB\right)=\frac{5}{6},P(A)=\frac{5}{6},P\left(B\right)=\frac{2}{3}$then $A$ and $B$ are.

1. Independent

2. Mutually exclusive

3. Mutually exhaustive

4. Dependent

Q. For any set $A,A\cap A^{\prime }\ne \varnothing .$

1. False
2. True

Q. For any set $A,A\cup A^{\prime }=U,$ where $U$ is the universal set.

1. True
2. False

Q.

If A, B and C are three events such that P(B) =$\frac{3}{4},P(A\cap B\cap C^{\prime })=\frac{1}{3}andP(A^{\prime }\cap B\cap C^{\prime })=\frac{1}{3},$ then $P(B\cap C)$ is equal to

1. $\frac{1}{12}$

2. $\frac{1}{6}$

3. $\frac{1}{15}$

4. $\frac{1}{9}$

Q. For any set $A,A\cup A^{\prime }=U,$ where $U$ is the universal set.

1. True
2. False

Q. For two sets $A=\{q,w,e,r,t,y\};B=\{r,t,y,u,i\},$ match the following.

1. $\{q,w,e\}$
2. $\{u,i\}$
3. $\{r,t,y\}$
4. $\{i,q,w,e,r,t,y,u\}$

Q.

If A, B and C are three events such that P(B) =$\frac{3}{4},P(A\cap B\cap C^{\prime })=\frac{1}{3}andP(A^{\prime }\cap B\cap C^{\prime })=\frac{1}{3},$ then $P(B\cap C)$ is equal to

1. $\frac{1}{12}$

2. $\frac{1}{6}$

3. $\frac{1}{15}$

4. $\frac{1}{9}$