To clarify, I'm assuming you want to know how many numbers between 7000 and 9999 lack the digit '7' in base 10. Of course, we can make a start by immediately reducing the range to 8000-9999. The first place can only be filled by one of the two digits 8 and 9.
The second, third and fourth can be filled by any of the ten digits 0-9. So, to find the probability that none of these digits are 7: 2/2 x 9/10 x 9/10 x 9/10 = 1458/2000. There are 2000 numbers in the range, so 1458 of these do not contain a figure 7.
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