Question

英语跟数学好的请进，请教概率问题！

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?

Answer 1

Q1：
(i) six defence players are chosen from twenty five hockey players，the possible is C(25,6)，then，five forward players are chosen from the other nineteen ，possible is C(19,5)；
so，there can be C(25,6)*C(19,5) teams;
(ii) six defence players are chosen from the ten available，the possible is C(10,6)，and，five forward players are chosen from the fifteen available，possible is C(15,5)；
so，there can be C(10,6)*C(15,5) teams
Q2:
(i) As Seventy percent of the first-year students are male,there are
12(40*30%) students are female from 40 first-year students. and seven of the female students graduated from high school the year before,so 5(12-7)female students took a “gap-year”；
To conclude, the probability is 1/8（5/40）that a randomly selected first-year student is both female and took a “gap-year”.
（ii）The probability is 1/2（half of 40）that given a randomly selected from 40 first-year students are “gap-year”ones, and the probability is 3/8[（1/2）*（15/20）]that given a randomly selected 40 first-year studes are male from “gap-year”ones.
So， the probability is 3/4 [（3/8）/（1/2）]that given a randomly selected student took a “gap-year” the student is male.
Q3：
(i) there are 22（13+12-3） red cards or face cards,so the probability is 11/27（22/54） that the card drawn is a red card or a face card.
（ii）the probability of having only odd numbers result when an unbiased six-sided die is rolled one time is 1/2（3/6）；
when an unbiased six-sided die is rolled five times， the probability of having only odd numbers result is 1/32（1/2*1/2*1/2*1/2*1/2）.

Answer 2

这么麻烦的题，不多给些分，谁会愿意帮你解答，还不够浪费时间呢

Answer 3

c25 11=25*24*23*22*21*20*19*18*17*16*15/11!
=25*23*3*19*17*8=600*391*19=7429*600=4457400

c10 5 *c15 6=6*7*8*9*10/5! 10*11*12*13*14*15/6!
=7*4*9+5*11*13*7=7*(36+715)=5257

(40-40*0.7-7)/40=1/8

(20-5)/20=3/4

1/4+3/13-3/52=11/26
1/2*1/2*1/2*1/2*1/2=1/32