Search any question & find its solution
Question:
Answered & Verified by Expert
If $A$ and $B$ are two independent events such that $P(\bar{A})=0.75, P(A \cup B)=0.65$ and $P(B)=x$, then find the value of $x$.
Options:
Solution:
2886 Upvotes
Verified Answer
The correct answer is:
$\frac{8}{15}$
Given, $P(\bar{A})=0.75, P(A \cup B)=0.65$ and $P(B)=x$ $P(A)=1-P(\bar{A})=1-0.75=0.25$
Also, $A$ and $B$ are independent.
$$
\begin{aligned}
& \Rightarrow P(A \cap B)=P(A) \cdot P(B)=0.25 x \\
& \text { Using } P(A \cup B)=P(A)+P(B)-P(A \cap B), \\
& \Rightarrow \quad 0.65=0.25+x-0.25 x \Rightarrow 0.40=0.75 x \\
& \Rightarrow \quad x=\frac{40}{75}=\frac{8}{15}
\end{aligned}
$$
Also, $A$ and $B$ are independent.
$$
\begin{aligned}
& \Rightarrow P(A \cap B)=P(A) \cdot P(B)=0.25 x \\
& \text { Using } P(A \cup B)=P(A)+P(B)-P(A \cap B), \\
& \Rightarrow \quad 0.65=0.25+x-0.25 x \Rightarrow 0.40=0.75 x \\
& \Rightarrow \quad x=\frac{40}{75}=\frac{8}{15}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.