Palindrome

Probability Level 3

Pick a random 5-digit number. What is the probability that the picked number is a palindrome?

The answer is 0.01.

2 solutions

Astro Enthusiast
Aug 7, 2014

There are 900 5-digit palindromes all in all and 90000 5-digit numbers. S0, 900/90000=0.01.

How do you know that there are exactly 900 5 digit palindromes???

Anuj Shikarkhane - 6 years, 10 months ago

the total number of three digit numbers is the number of 5 digit palindrome numbers as when we write a three digit number continued with its reversed order ,where the last digit is written only once, we get a 5 digit palindrome number . For eg., 123 and 321 when joined and eliminating the 1 three we get 12321 which is a palindrome number. If we don't eliminate one 3 , we get a six digit palindrome. And surprisingly all 2n and 2n-1 digit numbers have same number of palindrome numbers.

Vighnesh Raut - 6 years, 8 months ago

use filling slots methode, 5-digits polindromes: 9x10x10x1x1 (9, because a number doesn't begin with a zero (0); 1, because it is a palindrome so it has to be the exact same number like the first and the second one)

Catherine Charista - 6 years, 10 months ago

Milind Joshi
Aug 2, 2014

Total no of cases=9 * 9 * 9 * 9 * 9=59049......favorable cases=9 * 9 * 9* 1*1=729.....so pr obability=729/59049=0.0123

For 5-digit numbers, we require that they be of the form aaaaa, abbba or abcba, where a and b are as before and 0 <= c <= 9. We have 9 of the form aaaaa and 9 9 = 81 of the form abbba. Now c can be the same as a but must be different than b, so there are 9 9*9 = 729 palindromes of the form abcba, for a total of 9 + 81 + 729 = 819 5-digit palindromes no of 5 digit numbers=90000 P( that the picked 5 digit number is a palindrome)=0.0091 The answer 0.0102 is the probability that a picked number from 1-99999 is a palindrome.

Kushal Walia - 6 years, 10 months ago

Palindrome

The answer is 0.01.

2 solutions

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