# If A and B be two events associated with a random experiment

Question:

If A and B be two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and P $(A \cap B)=0.1$, find

(i) $P(\bar{A} \cap B)$

(ii) $P(A \cap \bar{B})$

Solution:

(i) Given : $P(A)=0.3, P(B)=0.2, P(A \cap B)=0.1$

To find $P(\bar{A} \cap B)$

Formula used: $P(\bar{A} \cap B)=\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})$

Substituting in the above formula we get,

$P(\bar{A} \cap B)=0.2-0.1$

$P(\bar{A} \cap B)=0.1$

$P(\bar{A} \cap B)=0.1$

(ii) Given : $P(A)=0.3, P(B)=0.2, P(A \cap B)=0.1$

To find : $P(A \cap \bar{B})$

Formula used : $P(A \cap \bar{B})=\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})$

Substituting in the above formula we get,

$P(A \cap \bar{B})=0.3-0.1$

$P(A \cap \bar{B})=0.2$

$P(A \cap \bar{B})=0.2$