英文跟数学好的请进,关于概率的问题
英文跟数学好的请进,关于概率的问题
Q1:Twenty five hockey players are available for selection for the state team. The team will have six defence players and five forward players.
(i) How many teams of eleven players are possible from the group of twenty five?
(ii) How many teams can be selected if five forwards are chosen from the ten available and six defence players are chosen from the fifteen available?
Q2 Among a group of 40 first-year students at a college campus half of them graduated from high school the year before, while the remainder took a “gap-year” graduating from high school two years before. Seventy percent of the first-year students are male and seven of the female students graduated from high school the year before.
(i) Find the probability that a randomly selected first-year student is both female and
took a “gap-year”.
(ii) What is the probability that given a randomly selected student took a “gap-year” the student is male?
Q3 (i) A card is drawn from an ordinary deck of playing cards that has been shuffled a number of times. What is the probability that the card drawn is a red card or a face
card (jack, queen or king)?
(ii) When an unbiased six-sided die is rolled five times what is the probability of having only odd numbers result?
1.从二十五名冰球运动员中挑选十一名队员组成州队,六名后卫,五名前锋.
(i)有多少种可能的组队方案?
(ii)若从十名队员中挑选五名作前锋,从其余十五名队员中挑选六名作后卫,则共有多少种可能的组队方案?
【解】
(i)C(11,25)
(ii)C(5,10)×C(6,15)
(* 具体数字请用计算器计算…… *)
2.在40名大学一年级新生中,有一半人是去年从高中毕业的,另一半则是前年高中毕业.一年级新生中有70%是男生,女生中有七人是去年高中毕业的.
(i)问,从这些一年级新生中随意挑选一名学生,这名学生是女生并且是前年高中毕业的概率是多少?
(ii)任意选出一名前年高中毕业的学生,此名学生是男生的概率是多少?
【解】
(i)由题意知,有28名男生,12名女生,女生中有7人是去年高中毕业,所以有5人是前年高中毕业.因此题目所求概率为 5/40=1/8
(ii)由题意知,有20名学生是前年高中毕业的,其中5名是女生,所以余下15名是男生,因此题目所求概率为 15/20=3/4
3.
(i)将一摞普通的扑克版洗过几次之后任抽一张,抽到红花色人头牌（J、Q、K）的概率是多少?
(ii)将一质地均匀的六面体骰子抛掷五次,每次都掷出奇数点的概率是多少?
【解】
(i)红花色人头牌共有3×2=6张,因此从全部52张牌中抽到这些牌的概率是 6/52=3/26
(ii)掷一次掷得奇数点的概率为½,因此连续五次均掷得奇数点的概率为 ½^5=1/32