Questions: Dice Rolls: You roll a pair of fair 6 -sided dice. Use the information below to answer the questions. a) First let's complete the sample space. The sample space is the set of all possible outcomes from a probability experiment. Therefore, we want to list all the outcomes if you roll a pair of fair 6 -sided dice. If you roll a 2 on the first die and a 4 on the second die then the entry will be 2,4. Fill in the blanks following this pattern (Hint: do not put any spaces in the blanks). 2nd roll=1 2nd roll=2 2nd roll=3 2nd roll=4 2nd roll=5 2nd roll=6 1st roll=1 1,1 1,2 1,3 1,4 1,5 1,6 1st roll=2 2,1 2,2 2,4 2,5 2,6 1st roll=3 3,2 3,3 3,4 3,5 3,6 1st roll=4 4,1 4,2 4,4 4,5 4,6 1st roll=5 5,1 5,2 5,3 5,4 5,5 5,6 1st roll=6 6,1 6,3 6,4 6,5 b) When you roll both dice and add up the pips (pips are the dots on the dice), what's the probability of getting a sum of 1 ? (round to 4 decimal places, if necessary) c) When you roll both dice and add up the pips, what's the probability of getting a sum of 5 ? (round to 4 decimal places, if necessary) d) When you roll both dice and add up the pips, what's the probability of getting a sum of 12? (round to 4 decimal places, if necessary)
Transcript text: Dice Rolls: You roll a pair of fair 6 -sided dice. Use the information below to answer the questions.
a) First let's complete the sample space. The sample space is the set of all possible outcomes from a probability experiment. Therefore, we want to list all the outcomes if you roll a pair of fair 6 -sided dice. If you roll a 2 on the first die and a 4 on the second die then the entry will be 2,4. Fill in the blanks following thispattern (Hint: do not put any spaces in the blanks).
\begin{tabular}{|l|r|r|r|r|r|r|}
\hline & 2nd roll=1 & 2nd roll=2 & 2nd roll=3 & 2nd roll=4 & 2nd roll=5 & 2nd roll=6 \\
\hline 1st roll=1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6 \\
\hline 1st roll=2 & 2,1 & 2,2 & $\square$ & 2,4 & 2,5 & 2,6 \\
\hline 1st roll=3 & & 3,2 & 3,3 & 3,4 & 3,5 & 3,6 \\
\hline 1st roll=4 & 4,1 & 4,2 & $\square$ & 4,4 & 4,5 & 4,6 \\
\hline 1st roll=5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6 \\
\hline 1st roll=6 & 6,1 & $\square$ & 6,3 & 6,4 & 6,5 & $\square$ \\
\hline
\end{tabular}
b) When you roll both dice and add up the pips (pips are the dots on the dice), what's the probability of getting a sum of 1 ? (round to 4 decimal places, if necessary)
$\square$
c) When you roll both dice and add up the pips, what's the probability of getting a sum of 5 ? (round to 4 decimal places, if necessary)
$\square$
d) When you roll both dice and add up the pips, what's the probability of getting a sum of 12? (round to 4 decimal places, if necessary)
$\square$
Solution
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