Question

3 Suppose a deck of playing cards has 52 cards, represented by the set C : C = {1C, 2C, . . . , 13C, 1D, 2D, . . . , 13D, 1H, 2H, . . . 13H, 1S, 2S, . . . , 13S}. 2 Here C, D, H, or S stands for the suit of a card: ”clubs”, ”diamonds”, ”hearts”, or ”spades”. Suppose five cards are drawn at random from the deck, with all possibilities being equally likely. (a) FLUSH is the event that all five cards have the same suit. Find P(FLUSH). (b) FOUR OF A KIND is the event that four of the five cards have the same number. Find P(FOUR OF A KIND).

Answer 1

TOPIC:Use of the Classical definition of probability.

52 cands tea e 1s, 2s ,-713 s LA, 2H , 13H, 一1 efine the eent as An dive cands have rhe- FLUSH Sinea, dhuve are total 52 cands i the deck, 5 cands can be drawn in 52 ways which are mutualy exelusiver oxhauws Hive ond equally likel Now, since dhere are total 4s suits, one suit can be selactel in 4wa and among the 13 cond the elected suit, s cauds can be selected in(13 wa sui t

den, the havoumable no. cares jow the cas es evene, v FLUSH', i 5 bル 13 52 5 001981 10. 0020 Roundedto our decimalb) have the ame mm b Observe diat, there are total 13 adro 4 nambus, ewhere the mumbers of the cand ane dhe dame . v :2 , 12, IH, 13), (, 22, 24, 23) (as, за, зн, 35), (13, 13 2, 13 , 13S Total (3posrible cages

So, drom these 13 hesile o drom these 13 poible caoes oma set of 4 mumbers cam be scleated in cand mumben con be any possible (52-9-48 Aelected numbers, which cam be selected iu uN Hene, the avounabe no can es 13 Clasic nigion 13 x /48 52 5 lo-00024