A palindromic number is a number that remains the same when its digits

Question

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}

MathRevolution · Accepted Answer

=>

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 * 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}.

Therefore, the answer is E.
Answer: E

pu230163 · Answer

Total 4-digit integers= 9999-1000+1= 9000.
There is only one palindromic number in evey 100 nos.
Therefore, total no.of palindromic= 90.
Probability= 90/9000=1/100.

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wilhelmus999 · Answer

You can choose first and second digit randomly (first digit not zero). Chance that third digit equals second: 1/10. Equally, chance that fourth digit = first digit: 1/10. That 0 is not possible for first digit doesn't matter: once chosen, chance that fourth is the same = 1/10. Check: other way round: choose 3rd and 4th at random. Chance that 1st equals 4th: 0 if 4th=0 and 1/9 if 4th not 0. So: chance that first equals 4th: 1/10 *0 + 9/10 * 1/9 = 1/10. So answer: 1/10 * 1/10 = 1/100

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ScottTargetTestPrep · Answer

Let’s determine the number of the 4-digit palindromes. Notice that a 4-digit number is a palindrome if it’s one of the following two formats: XXXX and XYYX where X and Y represent a digit and X ≠ Y and X is nonzero.

Format 1: XXXX

We see that X can be any digit from 1 to 9, inclusive; thus, there are 9 such numbers.

Format 2: XYYX

We see that X can be any digit from 1 to 9, inclusive, and Y can be any digit from 0 to 9, inclusive (excluding digit X), so that there are 9 choices for X and 9 choices for Y; thus, the number of 4-digit number in this format is 9 x 9 = 81.

Thus, there are a total of 9 + 91 = 90 numbers in both formats. Since there are 9000 four-digit numbers (1000 to 9999 inclusive), the probability of picking a 4-digit palindrome randomly is 90/9000 = 1/100.

Answer: E

MuditKapoor · Answer

Are 9999 oR 1111 also palindromic numbers?

Bunuel · Answer

Yes, 1111 and 9999 are palindromic numbers - they read the same forward and backward. Both are included when we count 4-digit palindromic numbers using the pattern ‘xyyx’. The calculation 9 * 10 = 90 already accounts for all such numbers from 1001 to 9999 that fit this format, including 1111 and 9999.

vijaymore148 · Answer

total 4 digit numbers -> 9*10*10*10 =  9000 
palindromic numbers -> baab -> now "a" can be any digit from 0-9 so " 10 possibilities " and "b" can be any digit from 1-9 so " 9 possibilities "
So total 4 digit palindromic numbers -> 10*9 =  90

therefore probability = 90/9000 = 1/100

impatientdude · Answer

Format will always be: 
XYYX where x can be equal to Y

You can choose X in 9C1 ways and Y in 10C1 ways. Total Palindromic numbers = 900.

P(E) = 900/9000 or 0.01

The_ashura · Answer

for palindrome-
say ABBA
Slot 1   -> Must be A
Slot 2   -> Must be B
Slot 3   -> Forced to be B
Slot 4   -> Forced to be A

Note
4 digit int will start from 1000 till 9999 (9000 integers)

A can be 9 integers(1to9), B can be 10 integers(0to9)

That makes 9x10

Out of total 9000 integers

Hence 90/900=1/100

Option E

A palindromic number is a number that remains the same when its digits

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A palindromic number is a number that remains the same when its digits

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