Q18: Guessing a 6-digit PIN when the first 4 digits are known

Each digit of a PIN is one of the 10 digits 0 to 9, and digits may repeat. The 4 known digits are right for certain, with probability 1 each. Each unknown digit is guessed right with probability $\frac{1}{10}$⁠.

Getting the fifth digit right and getting the sixth digit right are independent events $E$ and $F$⁠, so the probabilities multiply:

Another way: the last two digits can be $10 \times 10 = 100$ equally likely pairs, and only one of them is right.

Watch out: $\frac{1}{90}$ wrongly assumes the two digits are different, and $\frac{1}{81}$ wrongly uses only 9 choices for each digit.