In a certain collage, 4% of boys and 1% of girls

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Question:

          In a certain collage, 4% of boys and 1% of girls are taller than 1.75 metres, Furthermore, 60% of the students in the college are girls. A student is selected at random from the college and is found to be taller than 1.75 metres. Find the probability that the selected student is a girl.

Solution:

Let E = Student selected is girl

F = Student selected is boy

A = Student selected is taller than 1.75 metres

Now, P(E) = \frac{60}{100} = \frac{3}{5}

P(F) = \frac{40}{100} = \frac{2}{5}

P(A/E) = \frac{1}{100}, P(A/F) = \frac{4}{100}

probability that A student is selected at random from the college and is found to be taller than 1.75 metres and the the selected student is a girl

P(E/A) = \dfrac{P(E).P(A/E)}{P(E).P(A/E)+P(F).P(A/F)}

= \dfrac{\frac{3}{5}\times \frac{1}{100}}{\frac{3}{5}\times \frac{1}{100}+\frac{2}{5}\times \frac{4}{100}}

= \dfrac{\frac{3}{500}}{\frac{3}{500}+\frac{8}{100}}

= \dfrac{3}{500}\times \dfrac{500}{11} = \dfrac{3}{11}

Some other question

1 .Show that of all the rectangles inscribed in a given fixed circle

2. int root cotx + root tanx dx

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