What are the odds of winning the pokemon lottery?

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In the pokemon game owned by Nintendo, players are assigned a\( 5\)-digit trainer ID ranging from \(00000\) to \(65535\) which is randomly generated the moment they start the game. As they progress through the game, players can participate in the pokemon lottery, in which a lottery ticket with a random \(5\)-digit number ranging from \(00000\) to \(65535\) is drawn. Players are then awarded prizes based on the number of digits on the lottery ticket which matches their trainer ID. The prizes awarded are as follows:

\(2\) digits matched- PP Up

\(3\) digits matched- PP Max

\(4\) digits matched- Rare Candy

\(5\) digits matched- Master Ball

What is the probability of winning a Master Ball or Rare Candy in a single draw?

Details and assumptions:

  • You might want to use a calculator or Mathematical software to ease the computational process once you figure out the way to solve the problem.

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