概率问题1、2、3、4、5、6、7、8、9九个数第一个人随便抽三个,按从大到小的顺序排列第二个人也随便抽三个,按从大到小的顺序排列问第二个人最后的三位数比第一个人大的概率Bernardo

Question

概率问题
【 1、2、3、4、5、6、7、8、9】 九个数
第一个人随便抽三个,按从大到小的顺序排列
第二个人也随便抽三个,按从大到小的顺序排列
问第二个人最后的三位数比第一个人大的概率
Bernardo randomly picks 3 distinct numbers from the set {1,2,3,4,5,6,7,8,9} and arranges them in descending order to from a 3-digit number. Silivia randomly picks 3 distinct numbers from the set {1,2,3,4,5,6,7,8} and also arranges them in descending order to from a 3 digit number. What is the probability that Bernardo's number is larger than Solvia's number.
上面打错了，第二个人不能选9.
答案有5个选项： A）47/72 B) 37/56 C) 2/3 D)49/72 E) 39/56

Answer 1

We will separate this into two cases.
Case 1,Bernardo does not pick 9
This occurs with probability8*7*6/9*8*7=2/3 ..
Now,note that the probability of Bernardo's number being greater than Silvia's is the same as the probability of Silvia's being greater than Bernardo,which is half of 1-P(numbers of being equal) ..
Suppose Bernardo picks numbers a,b andc ..Then Silvia must pick the numbers a,b and c in some order,which can be done in 6 ways.Silvia can pick three numbers in 8*7*6 ways,so the probability of having the same 3 digit numbers is 1/56 and so the probability of Bernardo's number being greater is 2/3*55/112=55/168..
Case 2,Bernardo picks a 9
This occurs with probability 1-2/3=21/3 and Bernardo definitely has the larger number,so a total probability of 1/3
Thus,our answer is 55/168+1/3=37/56 ,so B .
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