Short questions {Total 34 marks] Q1[10 marks] Given two events A and B, state whether each of the following is possible or not possible. a] PUD = .46 b] Given that P(A)P(B) > 0, the events A and B are both mutually exclusive and independent. c] P(A H B) = 0.92. and PG] U B) = 0.42 d] lfA and B are mutually exclusive, then AC and BC are always mutually exclusive. e} P(A H B) = P(A)P(B) and PU?) I} P(B|A) Q2 [8 marks] In a large lecture, suppose 60% of the students are female and 40% are male. Records show that 15% of the female students and 20% of the male students are registered as parttime students. a] If a student is chosen at random from the lecture, what is the probability that the student studies part time? b] If a randomly chosen student studies parttime, what is the probability the student is male? Q3 [3 marks] Suppose that three fair dice are rolled. a] What is the probability of getting just one six? b] What is the probability of getting all three sixes? c] If you add all three dice together, how many times more likely are you to get 15 than 1?"? Q4 [8 marks] Julie passes through one traffic light on her daily commute to work. The light is set up on a one minute cycle: Red for 30 seconds, followed by Yellow for 5 seconds, followed by Green for 25 seconds (and the cycle restarts]. Each time Julie is exactly 10 meters from the light she decides whether or not to brake [she brakes if the light is red or yellow, and does not brake if the light is green}. a] What are the probabilities of the different light colours at the point Julie makes her decision whether or not to brake next Monday? b] What is the probability that she doesn't break? c] What is the probability she will break at the light for each of the next 3 consecutive workdays