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If an integer between 10 and 50, inclusive is chosen at random, what is the probability that the tens digit is greater than the units digit?
A. \(\frac{10}{41}\)
B. \(\frac{11}{41}\)
C. \(\frac{14}{41}\)
D. \(\frac{27}{41}\)
E. \(\frac{30}{41}\)
A. \(\frac{10}{41}\)
B. \(\frac{11}{41}\)
C. \(\frac{14}{41}\)
D. \(\frac{27}{41}\)
E. \(\frac{30}{41}\)
26 Nov 2021, 02:00
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Official Solution:
If an integer between 10 and 50, inclusive is chosen at random, what is the probability that the tens digit is greater than the units digit?
A. \(\frac{10}{41}\)
B. \(\frac{11}{41}\)
C. \(\frac{14}{41}\)
D. \(\frac{27}{41}\)
E. \(\frac{30}{41}\)
There are total of 41 integers between 10 and 50 inclusive (check the denominators in the options - all are 41).
We can simply list all the numbers which satisfy the condition:
If the tens digit is 1, there is one number: 10;
If the tens digit is 2, there are two numbers: 20, 21;
If the tens digit is 3, there are three numbers: 30, 31, 32;
If the tens digit is 4, there are four numbers: 40, 41, 42, 43;
If the tens digit is 5, there is one number: 50.
So, there are total of \(1+2+3+4+1=11\) such numbers.
The probability \(=\frac{11}{41}\)
Answer: B
If an integer between 10 and 50, inclusive is chosen at random, what is the probability that the tens digit is greater than the units digit?
A. \(\frac{10}{41}\)
B. \(\frac{11}{41}\)
C. \(\frac{14}{41}\)
D. \(\frac{27}{41}\)
E. \(\frac{30}{41}\)
There are total of 41 integers between 10 and 50 inclusive (check the denominators in the options - all are 41).
We can simply list all the numbers which satisfy the condition:
If the tens digit is 1, there is one number: 10;
If the tens digit is 2, there are two numbers: 20, 21;
If the tens digit is 3, there are three numbers: 30, 31, 32;
If the tens digit is 4, there are four numbers: 40, 41, 42, 43;
If the tens digit is 5, there is one number: 50.
So, there are total of \(1+2+3+4+1=11\) such numbers.
The probability \(=\frac{11}{41}\)
Answer: B
27 Oct 2025, 03:50
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@Bunuel
What about integers 11, 22, 33, 44? In these examples tens digit is equal to ones digit meaning these cases should be count as cases where tens digit is NOT greater than the unit digit.
My logic:
Total cases = Number where Unit digit is less than tens digit + Number where Unit digit is equal to Tens digit + Number where Unit digit is more than Tens digit.
Answer should be 15/41.
Please do correct me if I am thinking by my knee instead of using my mind.
AV
What about integers 11, 22, 33, 44? In these examples tens digit is equal to ones digit meaning these cases should be count as cases where tens digit is NOT greater than the unit digit.
My logic:
Total cases = Number where Unit digit is less than tens digit + Number where Unit digit is equal to Tens digit + Number where Unit digit is more than Tens digit.
Answer should be 15/41.
Please do correct me if I am thinking by my knee instead of using my mind.
AV
