1. In a student community, 40% of the students own a car and 60% of the students who own a car also own a bicycle. Also, 70% of the student community own a bicycle. Furthermore 30% of students who own a bicycle, also own a two-wheeler. Car owners do not own two-wheeler. Finally, 30% of the students own a two-wheeler. What is the probability that a randomly selected Student (a) owns a bicycle and a two-wheeler? (b) owns a car, but does not own a bicycle? (c) does not own any of the three? (d) owns a bicycle, but no car or two-wheeler? 2. University A and B play a series of games, with the first team to win 3 games being declared the winner of the series. Suppose that University A independently wins each game with probability 0.6. Find the conditional probability that University B wins the series given that it wins the first game