Please solve this.

2. Consider a standard 52 card deck of playing cards. In total there are four cards that are Aces1 four cards that are Kings, four cards that are Queens and four cards that are Jacks. The remaining 36 cards are four each of the nlm'ibers 2, 3, . . . 1 10. That is there are four cards that are trues, four cards that are threes etc. For this question1 suppose that we reduce the number of cards in the deck by I removing three of the Aces I removing two other cards that are not Aces The cards that are removed are discarded and are not used for the remainder of this question. As such we now have a deck that consists of just 47 cards. Suppose that a card is randomly drawn from this reduced sized deck. Let A1 denote the event that this card is an Ace. This card that was drawn from the deck of cards is now discarded and we continue with a deck of just 45 cards. Suppose that a second card is now randomly drawn from this 4-card deck and let A2 denote the event that this card is an Ace. Answer the following questions. (a) What is 151.49)? (4 marks) (b) Given that the rst card drawn was not an Ace1 what is the probability that the second card drawn is not an Ace? That is, using our notation, what is PMEIAE')? (c) What is the probability that both of the cards are not aces? That is, what is P(A" and A? )? Show your workings. (4 marks) (d) What is the probability that at least one of the cards is an ace? Show your workings. (4 marks) (e) Given that the first card drawn was an Ace, what is the probability that the second card drawn is not an Ace? (4 marks)