A player has to guess a 5-digit code in an attempt to unlock a prize. If the digits are to be
chosen from the integers between 0 and 6 and they can be repeated, what is the probability
that the player guesses the correct code on the first try?

Respuesta :

The probability that the player guesses the correct code on the first try is 1/16807

How to determine the probability that the player guesses the correct code on the first try?

The given parameters are:

  • Passcode = 5-digit
  • Possible digits = 0 - 6
  • Digits cannot be repeated

There are 7 digits between 0 and 6 (inclusive)

So, the total number of possible passwords is

Password = 7 * 7 * 7 * 7 * 7

This is so because each of the 5 digits can be any of the 5 digits.

This gives

Password = 16807

The probability that the player guesses the correct code on the first try is

P = 1/Password

This gives

P = 1/16807

Hence, the probability that the player guesses the correct code on the first try is 1/16807

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