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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Definitions:

Physical Inventory

The process of counting and verifying all physical goods and materials in stock by a business.

Shipping Costs

The expenses involved in transporting goods from one location to another, including freight charges, packaging, and handling fees.

Diseconomies of Scale

An economic concept where an increase in production leads to a rise in average costs per unit due to inefficiencies.

Economies of Scale

Cost advantages that a business can achieve by increasing the scale of production, leading to lower average costs per unit due to spread fixed costs and operational efficiencies.