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# 數學習題(幫幫我^^)並請附上算式，謝謝!

1. A history professor assigns ten books for reading but will only base his exam on five of them. A student selects only seven to read a) What is the probability that he would have read all of five books the exam is based on? b) What is the probability that three of the five are books he did not read?

2.Nine people are going on a skiing trip in three cars that will hold 2, 4, and 5 passengers, respectively. How many ways is it possible to transport the nine people to ski lodge using all cars?

3.A doctor has taken a vaccine from either storage unit P (which contains 30 current and 10 outdated vaccines), from unit Q (which contains 20 current and 20 outdated vaccines), or from unit R (which contains 20 current and 20 outdated vaccines ), but she is twice as likely to have taken it from unit P as from unit Q and twice as likely to have taken it from unit Q as from unit R.

a.What is the probability that the vaccine selected is an outdated one?

b.If the vaccine is outdated, what is the probability that it came from unit P?

### 2 Answers

- 堅持過好日子Lv 51 decade agoFavorite Answer
1. A history professor assigns ten books for reading but will only base his exam on five of them. A student selects only seven to read

a) What is the probability that he would have read all of five books the exam is based on?

從10本任意挑5本來讀的可能有 C(10，5) = 10*9*8*7*6/5*4*3*2*1 = 252種

挑7本，必挑中老師指定的5本，可看成先把那指定的5本抽出來，再從另外5本去挑2本，所以有C(5，2) x 1 =5*4/2*1 x 1 = 10 種

所以，機率是 10/252 = 5/126

b) What is the probability that three of the five are books he did not read?

有3本他沒挑到，也可看成5本指定的，他只挑到2本

也就是，5本指定的只中2本，另5本沒指定的都拿到

所以，這題的答案跟 (a)一樣

2.Nine people are going on a skiing trip in three cars that will hold 2, 4, and 5 passengers, respectively. How many ways is it possible to transport the nine people to ski lodge using all cars?

假設 A車最多可載2人，B車最多可載4人，C車最多可載5人

則每車至少1人(因為要有人開)，也就是從9人中挑3人出來「排列」(因為車子不同，所以用排列。 共有P(9，3)=540種方法。

接下來，把剩下的6個人分別排入ABC三車，共有下列這幾種聯集

(A，B，C)= (0，2，4)+ (0，3，3)+ (1，1，4)+ (1，2，3)+ (1，3，2)

方法有 C(6，2) + C(6，3)+ C(6，1)* C(5，1) + C(6，1)* C(5，2) + C(6，1)* C(5，3)

=15 + 20 + 6*5 +6*10 + 6*10

=15+20+30+60+60

=185 種

所以解答 = 504*185=93240 種

3.A doctor has taken a vaccine from either storage unit P (which contains 30 current and 10 outdated vaccines), from unit Q (which contains 20 current and 20 outdated vaccines), or from unit R (which contains 20 current and 20 outdated vaccines ), but she is twice as likely to have taken it from unit P as from unit Q and twice as likely to have taken it from unit Q as from unit R.

題目怪怪的，不知道是英文的問題還是數學的問題，「either」是二者擇一，卻有PQR三種儲存槽。but she is twice as likely to have taken it from unit P as from unit Q and twice as likely to have taken it from unit Q as from unit R.這一句也怪怪的，不會翻 ~ 不知道是不是我的問題還是題目的問題

a.What is the probability that the vaccine selected is an outdated one?

不知道是怎麼個取法，所以無法算

b.If the vaccine is outdated, what is the probability that it came from unit P?

vaccine是單數~~~~又難倒我了~~~ 從倀一個儲存槽裡抽一支疫苗嗎？

在P抽到的機率 = 10/40 = 1/4

在Q抽到的機率 = 20/40 =1/2

在R抽到的機率 = 20/40 =1/2

所以，由P來的機率是 (1/4)/(1/4 + 1/2 + 1/2) = 1/5

Source(s): 自己