F.5 MATHS -probabilities

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2011-02-04 12:28 am

1. Two cards are randomly drawn from a pack of 52 playing cards (without jokers) without replacement. Find the probabilities of the following events happening.
(a) The two cards are of the same unit
(b) The two cards are of different suits.
(c) There is at least one face card.
(A face card means K,Q,J)

回答 (1)

用戶2053

2011-02-04 1:49 am

✔ 最佳答案

a)P(The two cards are of the same unit)= P(Any 1st drawn card) * P(Any one of 3 other the same unit with the 1st card.)= (52/52) (3/51)= 3/51Alternatively :(13C1) (4C2) / 52C2= 3/51
b)P(The two cards are of different suits.)= P(Any 1st drawn card) * P(Any one of 13*3=39 other different suits cards.)= (52/52) * (39/51)= 39/51Alternatively :P(The two cards are of different suits.)= 1 - P(two cards with the same suit.)= 1 - (52/52)(12/51)= 39/51
c)P(at least one face card.)= 1 - P(two non-face cards)= 1 - (52 - 3*4) / 52](52 - 3*4 - 1) / 51= 1 - (40/52)(39/51)

= 1 - (10/13)(13/17)= 21/51

2011-02-03 23:29:57 補充：
a)

Answer 3/51 = 1/17

b)

Answer 39/51 = 13/17

c)

Answer 21/51 = 7/17

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