Final answer:
The random variable X represents the number of minutes to correctly guess a 3-digit garage code with a computer making one guess per minute, using a geometric distribution with a 1 in 1000 chance of success on each guess.
Step-by-step explanation:
The student asked how to calculate the random variable X, which represents the number of minutes it takes to guess the correct code from 1000 possible 3-digit garage codes, with a computer making a random guess every minute. To address this question:
Define the random variable X in words:
The random variable X represents the number of minutes it takes until the correct 3-digit garage code is guessed by making random guesses at the rate of one per minute.
Calculating Probability:
In the given scenario, every guess has a 1 in 1000 chance of being correct, assuming that each guess is independent and the process continues until success. If we are calculating the probability for exactly three guesses, then we are dealing with a geometric distribution, where probability mass function (PMF) for exactly x number of trials (minutes, in this context) is (1-p)^(x-1)*p, where p is the probability of success on a single trial (1/1000).
Distribution Choice:
Given that we are dealing with the number of trials until the first success, the appropriate distribution to use would be a geometric distribution or a discrete distribution given that time is measured in whole minutes here.