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A palindrome is a number that reads the same forward as backward. If a three-digit palindrome is randomly chosen, what is the probability that it is a multiple of \(8\) ?

 Jun 1, 2022
 #1
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There are 90 3-digit palindromes as follows:

 

(101 , 111 , 121 , 131 , 141 , 151 , 161 , 171 , 181 , 191 , 202 , 212 , 222 , 232 , 242 , 252 , 262 , 272 , 282 , 292 , 303 , 313 , 323 , 333 , 343 , 353 , 363 , 373 , 383 , 393 , 404 , 414 , 424 , 434 , 444 , 454 , 464 , 474 , 484 , 494 , 505 , 515 , 525 , 535 , 545 , 555 , 565 , 575 , 585 , 595 , 606 , 616 , 626 , 636 , 646 , 656 , 666 , 676 , 686 , 696 , 707 , 717 , 727 , 737 , 747 , 757 , 767 , 777 , 787 , 797 , 808 , 818 , 828 , 838 , 848 , 858 , 868 , 878 , 888 , 898 , 909 , 919 , 929 , 939 , 949 , 959 , 969 , 979 , 989 , 999)==90 Palindromes.

 

There are 10 palindromes that are multiples of 8 as follows:

(232, 272, 424, 464, 616, 656, 696, 808, 848, 888) >>Total = 10 palindromes.

 

Therefore, the probability is: 10 / 90 == 1 / 9

 Jun 1, 2022
 #2
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+1

A palindrome is a number that reads the same forward as backward. If a three-digit palindrome is randomly chosen, what is the probability that it is a multiple of  8?

 

 

1*1     none

2*2        132      172      

3*3     none

4*4        

5*5      none

6*6        816

7*7       none

8*8        808

9*9      none

 

808, 616, 424, 232,  848, 656,  464,  272,  888, 696

there 10 of them. ar mulples of 8

 

1*1    10 of those

2*2      10 of those

...

9*9    10 of those

 

90     3 digit palindromes

 

P(3 digit palindrome is multiple of 8) =    10/90  = 1/9

 

As always, you need to check.

 Jun 1, 2022

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