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Home » In a certain college, of boys and of girls are taller than meters. Furthermore, of the students are girls. If a student is selected at random and is taller than meters, what is the probability that the selected student is a girl?
In a certain college, 4 \% of boys and 1 \% of girls are taller than 1.75 meters. Furthermore, 60 \% of the students are girls. If a student is selected at random and is taller than 1.75 meters, what is the probability that the selected student is a girl?
Bayes’s Theorem and its Applications | CBSE | Class 12 | Exercise 30A | Maths | RS Aggarwal
In a certain college, 4 \% of boys and 1 \% of girls are taller than 1.75 meters. Furthermore, 60 \% of the students are girls. If a student is selected at random and is taller than 1.75 meters, what is the probability that the selected student is a girl?

Let, T :students taller than 1.75
B: Boys in class
G: Girls in class
We want to find P(G \mid T), i.e. probability that selected taller is a girl
\begin{array}{l} \mathrm{P}(\mathrm{G} \mid \mathrm{T})=\frac{\mathrm{P}(\mathrm{G}) \cdot \mathrm{P}(\mathrm{T} \mid \mathrm{G})}{\mathrm{P}(\mathrm{G}) \cdot \mathrm{P}(\mathrm{T} \mid \mathrm{G})+\mathrm{P}(\mathrm{B}) \cdot \mathrm{P}(\mathrm{T} \mid \mathrm{B})} \\ =\frac{\left(\frac{60}{100}\right)\left(\frac{1}{100}\right)}{\left(\frac{60}{100}\right)\left(\frac{1}{100}\right)+\left(\frac{40}{100}\right)\left(\frac{4}{100}\right)} \\ =\frac{60}{220}=\frac{3}{11} \end{array}
Therefore, the probability of selected taller student is a girl is \frac{3}{11}

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