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Let n be chosen at random from 1, 2, 3, ..., 100.  What is the probability that the units digit of 3^n is 3?

 May 7, 2020
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When 3^n is raised to powers of n ranging from 1 to 100, the following exponents all give a units digit of 3:

 

n=1; a=100;c=0; b=3^n;if(b%10 ==3, goto5, goto7);printn,", ",;c=c+1; n++;if(n<=100, goto3, 0);print"Total =",c

 

1 , 5 , 9 , 13 , 17 , 21 , 25 , 29 , 33 , 37 , 41 , 45 , 49 , 53 , 57 , 61 , 65 , 69 , 73 , 77 , 81 , 85 , 89 , 93 , 97 , Total = 25

 

Notice the pattern. Therefore, the probability is: 25 / 100 = 1/4

 May 7, 2020

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