Notes

Q12: 12 girls and 9 boys in the neighborhood club, and a team of 5
1. C(12+9,5)=C(21,5)（从21个里挑5个）=20349
2. 2 girls 3 boys C(12,2)(从12个里挑2个）*C(9,3)（从9个里挑3个）=66*84=5544
3. both boys and girls 总数20349-C(12,5)(全是男生的情况)-C(9,5)(全是女生的情况)=19431

Q11: For this problem, assume the balls in the box are numbered 1 through 7, and that an experiment consists of randomly selecting 2 balls one after another without replacement.
1. C(7,1)（从7个里挑1个）*C(6,1)（再从6个里挑1个）=42
2. 1/42
3. 1到7有3个even，4个odd，“at least one ball has an odd number?” 4/7（第一次拿到odd的可能性）+3/7（第一次没拿到odd）*4/6（第二次拿到odd）=6/7

Q10: a product code consists of a digit from the set {2,5,7} followed by 2 letters, not necessarily distinct, selected from the set {Y,J,C,M,P,A}. For example, 2JJ is such a code.
1. 3（数字3种可能）*6^2(字母36种可能）=108
2. 1/108
3. 1/3(数字只可能是2/5/7三种情况，其中含2的codes占三分之一）

Q9: 8 % withdraw, 16 % receive an A, 20 % receive a B, 34 % receive a C, 15 % receive a D, and 7 % receive an F.
1. A+B+C+D=0.85
2. 1-0.85=0.15
刚才Q10我第三问问的是code含2的可能性，你的可能不一样，忘发了，不好意思

Q8: S={O1,O2,O3,O4,O5,O6} and that w1=0.46,w2=0.15,w3=0.09,w4=0.03,w5=0.13,w6=0.14. Let E={O3,O5} and F={O1,O2}.
1. What is the value of Pr[E]? w3+w5=0.22
2. What is the value of Pr[F′]? w1+w2=0.61 1-0.61=0.39(问的是F一撇）

以下问题题目里的die打错了（我跟你不是一节课可能你的没打错），应该是dice，骰子，所以是1-6且概率想等

Q7：all the odd numbers are equally likely, all the even numbers are equally likely, the odd numbers are k times as likely as the even numbers, and Pr[1]=2/7.
奇数可能性一样，偶数可能性一样，所以Pr[1]=2/7=Pr[3]=Pr[5] 加起来等于6/7， 所以2，4，6加起来等于1/7，奇数可能性是偶数六倍，所以K=6

Q6: For this problem, assume that 1, 5, 4, and 6 are equally likely, a 3 is three times as likely as a 6, and a 2 is three times as likely as a 3.
假设1,5,4,6为一份，那3就是三份，2是九份，一共16份
1. w1= 1/16
2. w3=3/16
3. w2=9/16

Q5: all the odd numbers are equally likely to come up, all the even numbers are equally likely to come up, and the odd numbers are two times as likely to come up as the even numbers.
奇数（1，3，5）可能性一样，偶数（2，4，6）可能性一样，且奇数可能性是偶数两倍，所以奇数6份偶数3份，任意奇数=2/9，偶数=1/9