AMC 8 1985 Problem 22
AMC8 1985 年第 22 题
概率★★★☆☆
Assume every 7-digit whole number is a possible telephone number except those that begin with 0 or 1 . What fraction of telephone numbers begin with 9 and end with 0 ?
假设除了以 0 或 1 开头的号码外，所有七位正整数都是可能的电话号码。以 9 开头且以 0 结尾的电话号码占几分之几？
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
B
解析 · Solution
Solution 1
For a valid phone number, there are 10-2=8 possibilities for the first digit and 10 for each of the other 6 digits. Therefore, there are valid phone numbers.
For a phone number that starts with 9 and ends with 0, there are 10 possibilities for each of the middle 5 digits. Therefore, there are phone numbers that start with 9 and end with 0.
Therefore, of valid phone numbers start with 9 and end with 0.
Notice that selecting a random valid phone number is identical to randomly and independently selecting each digit of the phone number.
There are 10-2=8 possibilities for the first digit and 10 possibilities for the last digit, so the probability of selecting a phone number with first digit 9 and last digit 0 is .
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