An unfair 3-sided die is rolled twice. The probability of rolling a 3 is $0.5$, the probability of rolling a 1 is $0.25$, and the probability of rolling a 2 is $0.25$. Let $X$ be the outcome of the first roll and $Y$ the outcome of the second.
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Find the Joint Distribution of $X$ and $Y$ in a Table.
The outcome of $X = \{1,2,3\}$.
The outcome of $Y = \{1,2,3\}$.
Would I just make a table of all the roll possibilities?
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Find the Probability $\mathrm{P}(X+Y \geq 5)$.
The only roll that will make this is a 3 or a 2.
Should I just take the same of every possible roll to find this probability?
Best Answer
Sounds as though you are very much on the right track with this computation. Yes, make a table of all roll possibilities, and in each entry of the table (e.g. $X = i, Y = j$) find the probability of that outcome (since you are rolling two separate times, you can treat $X$ and $Y$ as independent random variables). Once you have your table, it will be easy to total up the probabilities for the outcomes which meet the condition $X+Y \ge 5$ (you can use the fact that the different outcomes which satisfy this condition are mutually exclusive).