# Determine a probability mass function

An urn contains 8 white balls and 4 black balls. Suppose you win 2 dollars when selecting a white ball and 3 dollars when selecting a black ball. If $X$ denotes your winnings when selecting a ball at random, determine the probability mass function of $X$.

Is the correct answer just $p(X=2) = \frac{2}{3}$ and $p(x=3) = \frac{1}{3}$? I'm sorry I am just getting back after many years away so I am unsure of some of these easier problems.

• Where do you need help? We're not a homework review service, but we will answer specific questions about difficulties you encounter in completing a question. See the information at self-study. – whuber Oct 8 '17 at 21:26
• X is either 2 or 3 so in the second case I think you mean P(i=3)=1/3. – Michael R. Chernick Oct 8 '17 at 21:37

Yeah that is the correct answer. $X$ can only take two values as you noted since it is the amount of winnings, and you defined each colour ball's specific winnings uniquely. No need to apologise, probability is always hard, especially after a long time without looking at questions.