1. Urn M contains 3 white and 4 black balls, Urn N contains five white and 4 black balls, Urn P contains 2 white and three black balls. An urn is randomly selected and a ball is drawn, calculate the probability of:

a) Be White.

b) Be Black.

c) that it comes from urn M if the ball is known to be white.

d) that it comes from urn M if the ball is known to be black.

2. In a school, 45% of the students are men, of whom 30% are taking the probability course while 40% of the women are taking probability. A student is selected at random, calculates the probability of:

a) that she is a woman if we know that she is studying probability.

b) be a man if he is not studying probability.

3. A bank classifies its clients according to their credit history as good or bad. The bank has observed that 1% of clients classified as good overdraw their credit while 10% of clients classified as bad do so. If 70% of customers are known to be considered good, find the probability that a randomly selected customer:

a) have a good record of knowing that he or she has overdrawn their account.

b) have a bad record knowing that he or she has not overdrawn their account.