Question

3. A hand of five cards is drawn simultaneously (without order or replacement) from a standard 52-card deck. Let A be the event that the hand includes four cards of the same kind, and let B be the event that at least two of the cards in the hand are of the same kind. a. Compute P(A). [5] b. Compute P(B). [5] c. Compute P(A|B). [5]

Answer 1

Page (0) P (A) IP four Card of Same kind) NO. of ways ए. iCards oot of of selecting =526 572 Now 니 Cards jo a kind a cloon any traink out of 13 ie (2,3,4,5,6,7,8 9, J, L, X,A) poly Now for this gank e out of a suits re have 3 Card from remaining ug Cards u84 Plata 134x *С, x ч r00024 5266

(9) P at least 2 cards are same) z 1- pl No Card is of same kind) PC No Card of saime kind) - 0 to cloose S distinct El to tho sanbe '366 2 pick suit for each rank ůs for each are Rank there available) 7) od Juss jo pood kind ways 136 XS ploty x 45 1366 x SG T fou as o 0.49292

(C) 7 ase of P (ALB) Plano P(B) pl u card of same kind & at & at least kind) P( 4 of samme kind) ) Common of borothy A & B PIA) same C P(ALBL 0.00024 P(A) P (B) 0.ooong