If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find

(i) P(A ∪ B) (ii) P(A ∩ B) (iii) P(A ∩ $\overline{B}$) (iv) P( $\overline{A}$ ∩ $\overline{B}$) [NCERT EXEMPLAR]

Q.

If A and B are mutually exclusive events such that P(A = 0.35 and P(B=0.45, find

(i) $P(A\cup B)$

(ii) $P(A\cap B)$

(iii) $P(A\cap \overline{B})$

(iv) $P(\overline{A}\cap \overline{B})$

Q. (a) If A and B be mutually exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find:
(i) P (A ∪ B)
(ii) $P(\overline{A}\cap \overline{B})$
(iii) P ($\overline{A}$ ∩ B)
(iv) P (A ∩ $\overline{B}$).

(b) A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35.
Find (i) P (A ∪ B)
(ii) $P(\overline{A}\cap \overline{B)}$
(iii) P (A ∩ $\overline{B}$)
(iv) P (B ∩ $\overline{A}$)

(c) Fill in the blanks in the following table:

	P (A)	P (B)	P (A ∩ B)	P (A ∪ B)
(i)	$\frac{1}{3}$	$\frac{1}{5}$	$\frac{1}{15}$	......
(ii)	0.35	....	0.25	0.6
(iii)	0.5	0.35	.....	0.7

Q. Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find
(i) P (A ∩ B)
(ii) P (A ∩ $\overline{B}$)
(iii) P ($\overline{A}$ ∩ B)
(iv) $P\left(\overline{A}\cap \overline{B}\right)$
(v) P (A ∪ B)
(vi) P (A/B)
(vii) P (B/A)

Q. $A\text{and}B$ are two events such that $P\left(A\right)=0.54,P\left(B\right)=0.69\text{and}P(A\cap B)=0.35$.
Find
$\left(i\right)$ $P(A\cup B)$
$\left(ii\right)$ $P(A^{\prime }\cap B^{\prime })$
$\left(iii\right)$ $P(A\cap B^{\prime })$
$\left(iv\right)$ $P(B\cap A^{\prime })$

Q.

(a) If A and B be mutualy exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find :
(i) $P(A\cup B)$ (ii) $P(\overline{A}\cup \overline{B})$

(iii) $P(\overline{A}\cup B)$ (iv) $P(A\cup \overline{B})$

(b) A and B are two events such that P(A)= 0.54, P(B) = 0.69 and $P(A\cup B)$ = 0.35. Find:

(i) $P(A\cup B)$ (ii) $P(\overline{A}\cup \overline{B})$

(iii) $P(A\cup \overline{B})$ (iv) $P(B\cup \overline{A})$

(c) Fill in the blanks in the following table :

P(A) P(B)

$P(A\cap B)$ $P(A\cup B)$

(i) $\frac{1}{3}$ $\frac{1}{5}$ $\frac{1}{15}$___

(ii) 0.35 ___ 0.25 0.6

(iii) 0.5 0.35 ___ 0.7