Happy Birthday Kostya!

Probability Level 2

Today is my friend Kostya's birthday, and this is my problem in his honour.

Andrei and Kostya sit in different rooms. Andrei writes a number from 1 to 8, inclusive, on a piece of paper. Kostya, with no knowledge of Andrei's number, also writes a number from 1 to 8 on his piece of paper. When both numbers have been written, the two pieces of paper are connected to form a two-digit number: Andrei's number goes first, Kostya's second. What is the probability that ab\overline{ab} is divisible by 9?

Details and Assumptions:

  • Both numbers can be the same.

  • Express your answer as a decimal.

  • There are a total of 8 numbers to choose from.


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