If I forgot the last two digits to my phone password and I can eliminate one of the choices for each question. How does this change the probability that both of my guesses are correct

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Answer:

Assuming that your phone password digits can be any number from 0 to 9, there are 10 possible choices for each digit. If you forgot the last two digits, there are 100 (10*10) possible combinations.

If you can eliminate one choice for each digit, then there are 9 choices left for each digit, so there are 81 (9*9) possible combinations.

The probability of guessing both digits correctly without eliminating any choices is 1/100 = 0.01 or 1%.

After eliminating one choice for each digit, the probability of guessing both digits correctly becomes 1/81, which is approximately 0.0123 or 1.23%.

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