Question

3. You have a standard deck of 52 playing cards. There are two colors (black and red) and four suits (spades are black, clubs are black, hearts are red, and diamonds are red). Each suit has 13 cards, in which there is an ace, numbered cards from 2 to 10, and three face cards (jack, queen, and king) a. You randomly draw and then replace a card. What's the probability it's an ace? What's the probability it's the 4 of spades? b. You randomly draw a card, and after replacing it, you draw another. Let A be the event that the card is a club; let B be the event that the card is red. What is P(A/B)? That is, what is the probability the second card is a club, given the first one was a red card? Are the two events independent? c. Repeat (b), this time assuming that when the first card is drawn, it is not replaced. Would this change your answer to (b) in terms of independence? d. Let C be the event a card is a face card, and let D be the event a card is black. You draw a single card. Evaluate P(C and D). Are the two events mutually exclusive?

Answer 1

PAGE: Total Cards - 2. Each suit have: 13 cards Black cards & 26 Red cards = 26 cal PC An Ace) = ? are 4 Ace in There duit, total lone Ace of each som . Plan Ace) = 52 I since the I so there card drawn and then replaced are 52 cards (Total) | P[ 4 of spade) = ? Each suit has one 4 So, | P (40fpadel=1 52 (b) If Abe the event that the card is club. Platz 13 19 B is the event that card annda with Camsvatnet is red.

PAGE: PCB) = 20 52 P(A/B - PLANB) PCB) 772 I PLANB) = Probability that card is club of red colour But the club has black colour. The events are independent as the occurence of one is not affecting the occurence of other. (C) without Replacement. P(A) = 13 = t. : PIB) : 26 P(AIB) PCAMB) P(B) CScanned with CamScanner

ces Plrace card') =PCC): 2 P ( Black card) - POD 26. P (cando = that is the Pccno) face card of Black colour 52: The two events are not mutually exclusive as they can occur at the same time. CScanned with CamScanner