In a certain college, 4% of boys and 1% of girls are taller than 1.75 metres. Further more, 60% of the students in the college are girls. A student is found to be taller than 1.75 metres. Find the probability that the selected students is girl.
Let us assume U1, U2 and A be the events as follows:
U1 = choosing Boy
U2 = choosing Girl
A = choosing student who is taller than 1.75 metres.
From the problem
⇒ 
⇒ 
⇒ P(A|U1) = P(Choosing boy who is taller than 1.75 metres)
⇒ 
⇒ P(A|U2) = P(Choosing girl taller than 1.75 metres)
⇒ 
Now we find
P(U2|A) = P(The chosen student is a girl taller than 1.75 metres)
Using Baye’s theorem:
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
∴ The required probability is 
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