a card is randomly taken from a full pack of 52 playing cards to check whether it is
diamond or not . it is then put back to the pack. a second card is taken and checked again whether it is diamond or not.
(a) use a tree diagram to show the probabilities of getting diamond.
(b)Find the probabilities of getting
(i) both cards are diamonds
(ii) one of the cards is a diamond
(iii) at least one card is a diamond
一條數學 急用20分
2015-03-30 4:14 am
回答 (2)
2015-03-30 4:41 am
✔ 最佳答案
a)1st card
／ ＼
／ ＼
♦ ♠♥♣
13/52 = 1/4 39/52 = 3/4
／ ＼ ／ ＼
／ ＼ ／ ＼
♦ ♠♥♣ ♦ ♠♥♣ ...... 2nd card
1/4 3/4 1/4 3/4
bi)
P(both cards are diamonds) = 1/4 × 1/4 = 1/16
bii)
P(one of the cards is a diamond) = 1/4 × 3/4 + 3/4 × 1/4 = 3/8
biii)
P(at least one card is a diamond)
= 1 - P(2 cards are not ♦ ) = 1 - 3/4 × 3/4 = 7/16
2015-03-29 22:28:26 補充：
1(a)是一幅樹形圖,表示了抽2張牌的所有可能情形。
上層表示第一張牌是♦ 的概率 = 13/52 = 1/4 及
第一張牌不是 ♦ (即是♠或♥或♣)的概率 = 39/52 = 3/4。
底層左方兩路徑分別表示第一張牌是♦後再抽第2張得到♦或不是♦的各自概率。
底層右方兩路徑分別表示第一張牌不是♦後再抽第2張得到♦或不是♦的各自概率。
利用此圖可很直觀地得到part (b)的計算。
2015-03-30 5:04 am
1(a)姐係點???
收錄日期: 2021-04-15 18:53:56
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150329000051KK00085