2. Consider a standard 52 card deck of playing cards. In total there are four cards that areAces, four cards that areKings, four cards that areQueensand four cards that areJacks. The remaining 36 cards are four each of the numbers 2, 3, ..., 10. That is there are four cards that aretwos, four cards that arethreesetc. For this question, suppose that we reduce the number of cards in the deck by

removing three of theAces

removing two other cards that are notAces

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. LetA1denote the event that this card is anAce. This card that was drawn from the deck of cards is now discarded and we continue with a deck of just 46 cards. Suppose that a second card is now randomly drawn from this 46-card deck and letA2denote the event that this card is anAce. Answer the following questions.

1. (a)What isP(AC1)?(4 marks)
2. (b)Given that the first card drawn was not anAce, what is the probability that the second card drawn is not anAce? That is, using our notation, what is
3. P(AC2|AC1)?
4. (4 marks)
5. (c)What is the probability that both of the cards are not aces? That is, what isP(AC1andAC2)? Show your workings.(4 marks)
6. (d)What is the probability that at least one of the cards is an ace? Show your workings.(4 marks)