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Home » In a class, of the boys and of the girls have an IQ of more than In this class, of the students are boys. If a student is selected at random and found to have and IQ of more than 150, find the probability that the student is a boy.
In a class, 5 \% of the boys and 10 \% of the girls have an IQ of more than 150 . In this class, 60 \% of the students are boys. If a student is selected at random and found to have and IQ of more than 150, find the probability that the student is a boy.
Bayes’s Theorem and its Applications | CBSE | Class 12 | Exercise 30A | Maths | RS Aggarwal
In a class, 5 \% of the boys and 10 \% of the girls have an IQ of more than 150 . In this class, 60 \% of the students are boys. If a student is selected at random and found to have and IQ of more than 150, find the probability that the student is a boy.

Let, I : students having IQ more than 150
B : Boys in the class
G: Girls in the class
We want to find P(B \mid I) i.e. probability that selected student having IQ greater than 150 is a boy
\begin{array}{l} P(B \mid I)=\frac{P(B) \cdot P(I \mid B)}{P(G) \cdot P(I \mid G)+P(B) \cdot P(I \mid B)} \\ =\frac{\left(\frac{60}{100}\right)\left(\frac{5}{100}\right)}{\left(\frac{60}{100}\right)\left(\frac{5}{100}\right)+\left(\frac{40}{100}\right)\left(\frac{10}{100}\right)} \\ =\frac{300}{300+400}=\frac{3}{7} \end{array}
Therefore, the probability that selected student having IQ greater than 150 is a boy is \frac{3}{7}

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