JEE Advanced 2010Paper 2
- Exam
- JEE Advanced
- Year
- 2010
- Paper
- Paper 2
- Subject
- Mathematics
- Chapter
- Probability
JEE Advanced 2010 · Paper 2 · Mathematics · Probability
A signal which can be green or red with probability (4)/(5) and...
A signal which can be green or red with probability and respectively, is received by station and then transmitted to station B. The probability of each station receiving the signal correctly is . If the signal received at station is green, then the probability that the original signal green is
Options
- A
- B
- C
- D
Correct answer
C.
Step-by-step solution
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}