Please answer these two questions step by step and some explanation

(5) [25 marks] You shuffle a deck of cards and deal your friend 5 cards. 0 What is the probability that they have exactly one ace in their 5 cards? [5 marks] 0 What is the probability that they have the ace of spades in their 5 cards? [5 marks] 0 Suppose your friend says, \"I have the ace of spades\". What is the probability that they have exactly two aces? [5 marks] 0 Suppose your friend says, \"I have at least one ace\". What is the probability that they have at least two aces? [10 marks] (6) [30 marks] Professor Plum, Mr. Green, and Miss Scarlet are all plotting to shoot Colonel Mustard. If one of these three has both an opportunity and the revolver, then that person shoots Colonel Mustard. Otherwise, Colonel Mustard escapes. Exactly one of the three has an opportunity with the following probabilities: Pr[Plum has the opportunity] = Pr[Green has the opportunity] = O'BIWO'BI [OOH Il Pr[Scarlet has the opportunity] = Exactly one has the revolver with the following probabilities, regardless of who has an opportunity: Pr[Plum has the revolver] = Pr[Green has the revolver] = Pr[Scarlet has the revolver] = OOII'G'JIGOOOIv-lh 0 Draw a tree diagram for this problem. Indicate edge and outcome probabilities. [15 marks] 0 What is the probability that Colonel Mustard is shot? [5 marks] 0 What is the probability that Colonel Mustard is shot, given that Miss Scarlet does not have the revolver? [5 marks] 0 What is the probability that Mr. Green had an opportunity, given that Colonel Mustard was shot? [5 marks]