1. A card is drawn at random from a pack of cards. Let A be the event that the card is red and B be the event that the card is king. Does the colour of card affect its probability of being a king?
2. In an entrance examination in Mathematics and Statistics, of the 120 students appeared for the examination, 65 passed in Mathematics, 75 passed in Statistics and 35 passed in both the tests. A student is selected at random. What is the probability that the student has (a) failed in both the tests (2) (b) passed in Mathematics given that the student has passed in one test atleast.