Test This Black Box

The black box shown above needs testing. Pressing the button generates a random number from 1 to 100. (I've added extra buttons to do 10 or 50 presses at a time.) The randomly selected number is not displayed to the user. There is a bug that will cause the box to go Poof! if one of the values is encountered.
How many times do you need to press the button to test 95% of the possible results?
Can you test all possible values?

If the number of unique values were not displayed, could you ever have any confidence that you have encountered 95% of the values?

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