Statistics Confusion Please Explain

Question

A state has a lottery game where a person picks one of the 1000? three-digit numbers between 000 and 999. The lottery selects a? three-digit number at random. With a bet of? $1, a person wins $500 if their number is selected and nothing? ($0) otherwise.
Let X denote the winnings for a $1 bet, so
x equals=$0 or x equals=$500
Construct the probability distribution for X.

Answer 1

A "probability distribution" is simply a frequency distribution (that is, a histogram) of the probabilities plotted against the outcome values.  For a probability distribution, the sum of all the probabilities equals one (cumulative certainty).  We have, for example, a "uniform distribution," a "normal distribution" (that is, a bell-shaped curve), a "Chi-square distribution," etc.

For this problem, there are two outcomes ($0 or $500) and the probability of each is based on a uniform probability distribution (that is, another probability distribution [a uniform one] that shows that outcomes of 000-999 are equally-likely).

 

So, here the frequency distribution is P vs. x  (where P is probability and x is $0 or $500).

 

          P vs. x    (Probability of winning either $0 or $500)

 

       1 |     * 0.999

          |     *

          |     *

          |     *

    P    |     *

          |     *

          |     *

          |     *

          |     *

          |     *                *  0.001

          ---------------------------------

               $0             $500

                       x