Search any question & find its solution
Question:
Answered & Verified by Expert
A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station $A$ and then transmitted to station B. The probability of each station receiving the signal correctly is $\frac{3}{4}$. If the signal received at station $B$ is green, then the probability that the original signal green is
Options:
Solution:
1103 Upvotes
Verified Answer
The correct answer is:
$\frac{20}{23}$
$\frac{20}{23}$
From the tree-diagram it follows that
$$
\begin{gathered}
P\left(B_G \mid G\right)=\frac{10}{16}=\frac{5}{8} \\
\therefore \quad P\left(B_G \cap G\right)=\frac{5}{8} \times \frac{4}{5}=\frac{1}{2} \\
P\left(G \mid B_G\right)=\frac{\frac{1}{2}}{P\left(B_G\right)}=\frac{1}{2} \times \frac{80}{46}=\frac{20}{23}
\end{gathered}
$$
$$
\begin{gathered}
P\left(B_G \mid G\right)=\frac{10}{16}=\frac{5}{8} \\
\therefore \quad P\left(B_G \cap G\right)=\frac{5}{8} \times \frac{4}{5}=\frac{1}{2} \\
P\left(G \mid B_G\right)=\frac{\frac{1}{2}}{P\left(B_G\right)}=\frac{1}{2} \times \frac{80}{46}=\frac{20}{23}
\end{gathered}
$$
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.