Q80 / 160 · AP EAMCET 2024 (22 May Shift 2) · Mathematics
A radar system can detect an enemy plane in one out of 10 consecutive scans. The probability that it cannot detect an enemy plane at least two times in four consecutive scans, is
- Correct answerA$0.9477$
- B$0.9523$
- C$0.9037$
- D$0.9063$
Solution
$\begin{gathered}
X_i= \begin{cases}1 ; & \text { if target is detected } \\
0 ; & \text { if target is not detected }\end{cases} \\
p(x)= \begin{cases}0.1 & ; \\
0.9=1 & x=0\end{cases}
\end{gathered}$
Now, each $\mathrm{X}_{\mathrm{i}}$ is independent trial with $p=0.1$ $P$ (target will be detected at least two times in 4 consecutive scans $)={ }^4 \mathrm{C}_2(0.1)^2(0.9)^2+{ }^4 \mathrm{C}_3(0.1)^3(0.9)^1$ $+{ }^4 \mathrm{C}_4(0.1)^4(0.9)^0=0.0523$ So, required probability $=1-0.0523=0.9477$
Now, each $\mathrm{X}_{\mathrm{i}}$ is independent trial with $p=0.1$ $P$ (target will be detected at least two times in 4 consecutive scans $)={ }^4 \mathrm{C}_2(0.1)^2(0.9)^2+{ }^4 \mathrm{C}_3(0.1)^3(0.9)^1$ $+{ }^4 \mathrm{C}_4(0.1)^4(0.9)^0=0.0523$ So, required probability $=1-0.0523=0.9477$
Hence, the correct answer is option: 'A'.