Question

In a school 5% boys and 2% girls have wight more than 50Kg. Furthermore 20% of the students in the school are boys. A student is selected at random from the schooland is found to weigh 60Kg. Find the probability that the selected studenrt is a girl.

Answer 1

It is a question of bayes theorem
Let the event of having weight more than 50kg be E.
Probability of being a boy P(B) = 0.2
Probability of being a girl P(G) = 0.8
And the probability of weight of girl more than 50 kg = P(E/G) = 0.02
And the probability of weight of boy more than 50 kg = P(E/B) = 0.05

Hence the probability of student selected having weight more than 50 kg is a girl is = P(G/E)
So P(G/E) = $\frac{P\left(G\right)\times P(E/G)}{P\left(G\right)\times P(E/G)+P\left(B\right)\times P(E/B)}$
= $\frac{0.02\times 0.8}{0.02\times 0.8+0.2\times 0.05}=\frac{8}{13}\left(Ans\right)$