Q79 / 160 · TS EAMCET 2018 (04 May Shift 2) · Mathematics
In a classroom $5 \%$ of the boys and $2 \%$ of the girls are taller than $1.6 \mathrm{~m}$. The class consists of $60 \%$ girl students. The probability that a randomly selected student is taken than $1.6 \mathrm{~m}$ is
- A$\frac{121}{125}$
- B$\frac{5}{8}$
- C$\frac{3}{8}$
- Correct answerD$\frac{4}{125}$
Solution
Probability of boys taller than $\mathrm{l} \cdot 6 \mathrm{mt}=\frac{5}{100} \Rightarrow \frac{1}{20}$ Probability of girls taller than $1 \cdot 6 \mathrm{mt}=\frac{2}{100} \Rightarrow \frac{1}{50}$
$$
\begin{array}{rlrl}
& P_x=P_B \cdot P_{\frac{t}{B}}+P_g \cdot P_{\frac{t}{g}} & =\frac{40}{100} \cdot \frac{1}{20}+\frac{60}{100} \cdot \frac{1}{50} \\
\Rightarrow \quad \frac{2}{100}+\frac{12}{1000} & \Rightarrow \frac{-(20)+12}{1000} \\
\Rightarrow \quad & \frac{32}{1000} & =\frac{4}{125}
\end{array}
$$
Hence, the correct answer is option: 'D'.