In a certain college, 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.

Explanation

Let `P(S)` is the probability of selecting a student with more than `1.75` m height.

Let `P(B)` is the probability of selecting a boy and `P(G)` is the probability of selecting a girl.

Then, required probabilty will be `P(G/S)`.

`:. P(G/S) = (P(S/G)*P(G))/(P(S/G)*P(G)+P(S/B)*P(B))`

Here, `P(S/G) = 1/100, P(S/B) = 4/100`

`P(B) = 40/100 and P(G) = 60/100`

So, putting these values,

`P(G/S) = (1/100*60/100)/(1/100*60/100+4/100*40/100)`

...