(Solved): 3. A class had two sections. Section 1 had 55 students of whom 10 received A grades. Section 2 had ...

3. A class had two sections. Section 1 had 55 students of whom 10 received A grades. Section 2 had 45 students of whom 11 received A grades. If one of the 100 students is taken at random, determine the following probabilities: Define events: - \( S 1= \) denote the event where the student is from Section 1 - \( \mathbf{A}= \) denote the event were the student received an \( \mathbf{A} \) a. The probability which the student was in Section 1. b. The probability which the student received an A. c. The probability which the student received an A if the student is known to be on Section 1. d. The probability that the student was in Section 1 if its known that the student received an A.