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An integer greater than 9 and less than 100 is randomly chosen. What is the probability that its digits are greater than 7?

 Dec 27, 2020
 #1
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I assumed you meant "SUM of its digits > 7": If that is the case, then you have:

 

(1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 18)>>Total = 90 such sums

 

Probability = 62 / 90 ==31 / 45

 Dec 27, 2020
 #2
avatar+112823 
+1

A different interpretation.

 

10 to 99    is   90 numbers in total

which ones have BOTH digits either 8 or 9      

only 88, 89,98 and 99

 

so that is 4/90 

 Dec 28, 2020

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