In a certain college 4% of the boys and 1% of the girls are taller than 1.8 mts. further more 60% of the students are girls, if a student selected at random is taller than 1.8mts, what is the probability than the students was a boy? justify your answer.

Solution: Let total number of students in a college = 1000

60% students are girls.

$\therefore$ No. of girls students = 600

$\therefore$ No. of boy students = 400

4% of 400 are taller than 1.8 mts

$= 400 \times \frac{4}{100} = 16$

1% of 600 are taller than 1.8 mts

$= 600 \times \frac{1}{600} = 6$

From the above information we can

$\therefore$ Probability that selected student is a boy = $\frac{16}{22} = 0.727$