A class had two setions Section I had 55 students of whom 10

A class had two setions. Section I had 55 students of whom 10 received A grades. Section II had 45 students of whom 11 received A grades. Now 1 of the 100 students is chosen at random, with each being equally likely to be chosen.

a) what is the probability that the student was in section I?

b) what is the probability that the student received an A grade?

c) what is the probability that the student received an A grade if the student is known to have been in section I?

d) what is the probability that the student was in section I if the student is known to have received an A grade?

Solution

a) Probaility of chosen is form section I = 55 C 1 = 100 C 1 = 55/100 = 0.55

b)
P( Chosen student has A grade) = Pick an A grade student/ 100 C 1 = 21 C 1 / 100 = 21/100 = 0.21

c)
P(Student received A grade given that He is from Section I) = P( A grade / Section I) = P( A n Section I) / P( Section I) = 10 / 55 = 0.1818

d)
P(Student is Section I and given that he received A grade ) = P( A grade / Section I) = P( A n Section I) / P( A grade) = 10 / 21 = 0.4761