Question

Consider a standard 52-card deck of cards. In particular (for those unfamiliar with playing cards), the deck contains 4 aces, 4 kings, 4 queens, 4 Jacks, 4 10's, 4 94, 4 84, 4 7's, 4 6's, 4 5's, 4 4's, 4 3, and 4 2's, where for each type of card (for example ace), one of the 4 copies is of suit club, one is of suit heart, one is of suit spade, and one is of suit diamond. Consider the following experiment E Experiment E: I shuffle the deck of cards, and flip over the top two cards. I record which cards these were, calling the top card ci, and the second-from-the-top card c2 Consider the following events, given as English questions Event A: Was c the ace of spades? *Event B: Was c2 an ace? a. (4 points) What is P(B)? b. (4 points) What is P(AUB)?

Answer 1

i-e· c, and C2 au fur med nespectively ent A Event B : №AG an ace ? Has ,hu ace of pades 52 was not an +c was on a c was an au) P(G, was an acu) 51 52 51 52 51- (51)(13) 51 52 51 (51)(52) 663-54 6C3 I- 54 (8') 60 g 66 3 = 52 663 P( , was ace of spa d and G uras am aa) 52 5

P(B/A) (A) 缶) (h) r(AUB) し+て13 5 2 51 643 = 0.01920.0814 0. 6011 : 0-101