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,
$P(A \cap \bar{B})=0.3-0.1$
$P(A \cap \bar{B})=0.2$
$P(A \cap \bar{B})=0.2$