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18 Jun 2018, 00:36
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A palindromic number is a number that remains the same when its digits are reversed. For example, 16461 is a palindromic number. If a 4-digit integer is selected randomly from the set of all 4-digit integers, what is the probability that it is palindromic?
A. \(\frac{1}{20}\)
B. \(\frac{1}{50}\)
C. \(\frac{1}{60}\)
D. \(\frac{1}{90}\)
E. \(\frac{1}{100}\)
A. \(\frac{1}{20}\)
B. \(\frac{1}{50}\)
C. \(\frac{1}{60}\)
D. \(\frac{1}{90}\)
E. \(\frac{1}{100}\)
18 Jun 2018, 00:36
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Official Solution:
A palindromic number is a number that remains the same when its digits are reversed. For example, 16461 is a palindromic number. If a 4-digit integer is selected randomly from the set of all 4-digit integers, what is the probability that it is palindromic?
A. \(\frac{1}{20}\)
B. \(\frac{1}{50}\)
C. \(\frac{1}{60}\)
D. \(\frac{1}{90}\)
E. \(\frac{1}{100}\)
4-digit palindromic numbers have the form \(xyyx\), where \(x\) is one of values 1, 2, …, 9 and \(y\) is one of values 0, 1, 2, …, 9.
So, there are 9 x 10 = 90 four-digit palindromic numbers.
The total number of 4-digit numbers between 1000 and 9999, inclusive, is 9000 ( = 9999 – 1000 + 1 ).
Therefore, the probability that the selected 4-digit is palindromic is \(\frac{90}{9000} = \frac{1}{100}\).
Answer: E
A palindromic number is a number that remains the same when its digits are reversed. For example, 16461 is a palindromic number. If a 4-digit integer is selected randomly from the set of all 4-digit integers, what is the probability that it is palindromic?
A. \(\frac{1}{20}\)
B. \(\frac{1}{50}\)
C. \(\frac{1}{60}\)
D. \(\frac{1}{90}\)
E. \(\frac{1}{100}\)
4-digit palindromic numbers have the form \(xyyx\), where \(x\) is one of values 1, 2, …, 9 and \(y\) is one of values 0, 1, 2, …, 9.
So, there are 9 x 10 = 90 four-digit palindromic numbers.
The total number of 4-digit numbers between 1000 and 9999, inclusive, is 9000 ( = 9999 – 1000 + 1 ).
Therefore, the probability that the selected 4-digit is palindromic is \(\frac{90}{9000} = \frac{1}{100}\).
Answer: E
29 Oct 2018, 12:31
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Here is a better explanation.
Total no. of outcomes= 9999-999=9000 numbers of 4 digits
Favorable outcomes= 9C1 x 10C1 x 1C1 x 1C1=90
Hence , probability = 90/9000=1/100
Total no. of outcomes= 9999-999=9000 numbers of 4 digits
Favorable outcomes= 9C1 x 10C1 x 1C1 x 1C1=90
Hence , probability = 90/9000=1/100
