Question 2: a) P (K1) 2 2 kings remaining is 47 cards in the deck. - P (K1) = 2/47 Therefore P (K1) = 2/47 b) P (K2| K1) 2 1 king left in a deck of 46 cards. Therefore P (K2 | K1) = 1/46 c) P (K1 and K2) 2 P (K1 and K2) = P (K1) x P (K2/K1) =2/47 x 1/46 Therefore, (K1 and K2) = 2/2162 d) P (K3c | K1 and K2) 2 The first two cards drawn were kings, there are no kings left in the deck of 45 cards Therefore P (K3c | K1 and K2) = 1 e) P (K1 and K2 and K3c) 2 We calculated P (K1 and K2) = 2/2162 in part c) P (K1 and K2 and K3c) = P (K1 and K2) x P (K3c|K1 and K2) STAIDCT Assignment 4 Name: Maria Magdau Student Number:22331393 P (K3c | K1 and K2) = 1 P (K1 and K2 and K3c) = 2/2162 x 1 Therefore, P (K1 and K2 and K3c) = 2/21622. Consider a standard 52 card deck of playing cards. In total there are four cards that are Aces, 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 numbers 2, 3, ..., 10. That is there are four cards that are twos, four cards that are threes ete. For this question, suppose that we reduce the number of cards in the deck by o removing two of the Kings e removing three other cards that are not Kings 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 K; denote the event that this card is a King. 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 let K3 denote the event that this card is a King. 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 third card is now randomly drawn from this 45-card deck and let K3 denote the event that this card is a King. Answer the following questions. (a) What is P(K1)? (4 marks) (b) Given that the first eard drawn was a King, what is the probability that the second card drawn is a King? That is, using our notation, what is P K1)? (4 marks) (c) What is the probability that the first card drawn is a King and the second card drawn is a King? That is, what is P(K; and K3)? Show your workings. (4 marks) (d) Given that the first card drawn is a King and the second card drawn is a King, what is the probability that the third card drawn is not a King? That is, what is P {K:{Kl and K'g})? (4 marks) (e) What is the probability that the first two cards drawn are Kings and the third card drawn is not a King? That is, what is P(K; and K5 and K)? Show your workings. (4 marks)