f6M1數學題一問?20點

Five cards are randomly drawn from 52 playing cards.
1.Find expected number of face cards drawn if cards are drawn with
replacement.
Expected number
= 5(3*4/52)
= 15/13
2.Find expected number of face cards drawn if cards are drawn without
replacement.
Expected number
= (1)(12*40*39*38*37)/(52*51*50*49*48) + (2)(12*11*40*39*38)/(52*51*50*49*48) + (3)(12*11*10*40*39*38)/(52*51*50*49*48) + (4)(12*11*10*9*40)/(52*51*50*49*48) + (5)(12*11*10*9*8)/(52*51*50*49*48)
= 6922/7735


2011-09-10 13:01:14 補充：
2.Find expected number of face cards drawn if cards are drawn without
replacement.
Expected face
= 1 * 12C1 * 40C4/52C5 + 2 * 12C2 * 40C3/52C5 + 3 * 12C3 * 40C2/52C5 + 4 * 12C4 * 40C1/52C5 + 5 * 12C5/52C5
= 15/13