Question

in a game, a player has to guess a 3 - digit code in an attempt to unlock a trunk containing a prize. if the digits are to be chosen from the integers between 0 and 9 and they can be repeated, what is the probability that the player guesses the correct code on the first try?
\\(\frac{1}{9}\\)
\\(\frac{1}{30}\\)
\\(\frac{1}{1000}\\)
\\(\frac{1}{729}\\)

Explanation:

Step1: Calculate total number of possible codes

Each digit of the 3 - digit code can be chosen from 10 integers (0 - 9). By the multiplication principle, the total number of possible 3 - digit codes is $10\times10\times10=1000$.

Step2: Calculate probability of guessing correctly on first try

The probability $P$ of an event is the number of favorable outcomes divided by the number of total outcomes. There is only 1 correct code, so $P=\frac{1}{1000}$.

Answer:

$\frac{1}{1000}$