Question

If two events from a random experiment are $A$ and $B$,
$P(A)=0.25$, $P(B)=0.5$and $P(A\cap B)=0.15$, then $P(A\cap \overline{B})=?$
A. $0.1$
B. $0.35$
C. $0.15$
D. $0.6$

Answer 1

Hint: In this question, we are to find the probability of $A$ and $\overline{B}$. The addition theorem of probability is used to find the required probability. All the given values are substituted in the addition theorem of probability to find the required probability

Formula used: The probability is calculated by,
$P(E)=\dfrac{n(E)}{n(S)}$
If there are two events in a sample space, then the addition theorem on probability is given by
$P(A+B)=P(A)+P(B)-P(A\cap B)$
And
$P(A\cap \overline{B})=P(A)-P(A\cap B)$
When two events happen independently, the occurrence of one is not impacted by the occurrence of the other.
For the events $A$ and $B$, $P(A\cap B)=P(A)\cdot P(B)$ if they are independent and $P(A\cap B)=\Phi $ if they are mutually exclusive.

Complete step by step solution: As a result, incidents $A$ and $B$ are two from a random experiment,
$P(A)=0.25$
\[P(B)=0.5\]
\[P(A\cap B)=0.15\]
Then, the required probability is
$\begin{align}
  & P(A\cap \overline{B})=P(A)-P(A\cap B) \\
 & \text{ }=0.25-0.15 \\
 & \text{ }=0.1 \\
\end{align}$

Thus, Option (A) is correct.

Note: In this question, the addition theorem on probability is applied for finding the required probability. By substituting the appropriate values, the required probability is calculated. Here we may go wrong with the complimented probability. The actual probability must be calculated.