Make a Probability Distribution for the Given Set of Events $( 1,1 ) \quad ( 1,2 ) \quad ( 1,3 ) \quad ( 1,4 ) \quad ( 1,5 ) \quad ( 1,6 )$

question 8

Multiple Choice

Make a probability distribution for the given set of events.
-When two fair dice are rolled, 36 equally likely outcomes are possible as shown below. $( 1,1 ) \quad ( 1,2 ) \quad ( 1,3 ) \quad ( 1,4 ) \quad ( 1,5 ) \quad ( 1,6 )$
$( 2,1 ) \quad ( 2,2 ) \quad ( 2,3 ) \quad ( 2,4 ) \quad ( 2,5 ) \quad ( 2,6 )$
$( 3,1 ) \quad ( 3,2 ) \quad ( 3,3 ) \quad ( 3,4 ) \quad ( 3,5 ) \quad ( 3,6 )$
$( 4,1 ) \quad ( 4,2 ) \quad ( 4,3 ) \quad ( 4,4 ) \quad ( 4,5 ) \quad ( 4,6 )$
$( 5,1 ) \quad ( 5,2 ) \quad ( 5,3 ) \quad ( 5,4 ) \quad ( 5,5 ) \quad ( 5,6 )$
$( 6,1 ) \quad ( 6,2 ) \quad ( 6,3 ) \quad( 6,4 ) \quad ( 6,5 ) \quad ( 6,6 )$ Find the probability distribution for the product of the two numbers that appear when two fair dice are rolled.

• A)
• \(\begin{array}{r|r}
• \text { Product } & \text { Probability } \\
• \hline 1 & 1 / 18 \\
• 2 & 1 / 18 \\
• 3 & 1 / 18 \\
• 4 & 1 / 18 \\
• 5 & 1 / 18 \\
• 6 & 1 / 18 \\
• 8 & 1 / 18 \\
• 9 & 1 / 18 \\
• 10 & 1 / 18
• \end{array}\)
• \(\begin{array}{r|r}
• \text { Product } & \text { Probability } \\
• \hline 12 & 1 / 18 \\
• 15 & 1 / 18 \\
• 16 & 1 / 18 \\
• 18 & 1 / 18 \\
• 20 & 1 / 18 \\
• 24 & 1 / 18 \\
• 25 & 1 / 18 \\
• 30 & 1 / 18 \\
• 36 & 1 / 18
• \end{array}\)
• B)
• \(\begin{array}{r|r}
• \text { Product } & \text { Probability } \\
• \hline 2 & 1 / 36 \\
• 3 & 1 / 18 \\
• 4 & 1 / 12 \\
• 5 & 1 / 9 \\
• 6 & 5 / 36
• \end{array}\)
• \(\begin{array}{r|r}
• \text { Product } & \text { Probability } \\
• \hline 7 & 1 / 6 \\
• 8 & 5 / 36 \\
• 9 & 1 / 9 \\
• 10 & 1 / 12 \\
• 11 & 1 / 18 \\
• 12 & 1 / 36
• \end{array}\)
• C)
• \(\begin{array}{r|r}
• \text { Product } & \text { Probability } \\
• \hline 2 & 1 / 18 \\
• 3 & 1 / 18 \\
• 4 & 1 / 12 \\
• 5 & 1 / 18 \\
• 6 & 1 / 9 \\
• 8 & 1 / 18
• \end{array}\)
• \(\begin{array}{r|r}
• \text { Product| } & \text { Probability } \\
• \hline 10 & 1 / 12 \\
• 12 & 1 / 9 \\
• 15 & 1 / 12 \\
• 18 & 1 / 12 \\
• 20 & 1 / 12 \\
• 24 & 1 / 12 \\
• 30 & 1 / 18
• \end{array}\)
• D) \[\begin{array}{l}
• \begin{array} { r | r r | r }
• \text { Product } & \text { Probability } & \text { Product } & \text { Probability } \\
• \hline 1 & 1 / 36 & 12 & 1 / 9 \\
• 2 & 1 / 18 & 15 & 1 / 18 \\
• 3 & 1 / 18 & 16 & 1 / 36 \\
• 4 & 1 / 12 & 18 & 1 / 18 \\
• 5 & 1 / 18 & 20 & 1 / 18 \\
• 6 & 1 / 9 & 24 & 1 / 18 \\
• 8 & 1 / 18 & 25 & 1 / 36 \\
• 9 & 1 / 36 & 30 & 1 / 18 \\
• 10 & 1 / 18 & 36 & 1 / 36
• \end{array}
• \end{array}\]

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