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 41

Multiple Choice

Make a probability distribution for the given set of events.
-When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. $( 1,1 ) \quad ( 1,2 ) \quad ( 1,3 ) \quad ( 1,4 ) \quad ( 1,5 ) \quad ( 1,6 )$
$( 2,1 ) \quad ( 2,2 ) \quad ( 2,3 ) \quad ( 2,4 ) \quad ( 2,5 ) \quad ( 2,6 )$
$( 3,1 ) \quad ( 3,2 ) \quad ( 3,3 ) \quad ( 3,4 ) \quad ( 3,5 ) \quad ( 3,6 )$
$( 4,1 ) \quad ( 4,2 ) \quad ( 4,3 ) \quad ( 4,4 ) \quad ( 4,5 ) \quad ( 4,6 )$
$( 5,1 ) \quad ( 5,2 ) \quad ( 5,3 ) \quad ( 5,4 ) \quad ( 5,5 ) \quad ( 5,6 )$
$( 6,1 ) \quad ( 6,2 ) ( 6,3 ) \quad ( 6,4 ) \quad ( 6,5 ) \quad ( 6,6 )$ Let X denote the smaller of the two numbers. If both dice come up the same number, then X equals that common value. Find the probability distribution of X. Leave your probabilities in fraction
Form.

• A)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 1 & 5 / 18 \\
• 2 & 1 / 4 \\
• 3 & 7 / 36 \\
• 4 & 5 / 36 \\
• 5 & 1 / 9 \\
• 6 & 1 / 36
• \end{array}\)
• B)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 1 & 11 / 36 \\
• 2 & 1 / 4 \\
• 3 & 7 / 36 \\
• 4 & 5 / 36 \\
• 5 & 1 / 12 \\
• 6 & 1 / 36
• \end{array}\)
• C)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 1 & 1 / 6 \\
• 2 & 1 / 6 \\
• 3 & 1 / 6 \\
• 4 & 1 / 6 \\
• 5 & 1 / 6 \\
• 6 & 1 / 6
• \end{array}\)
• D)
• \(\begin{array}{r|r}
• x & P(X=x) \\
• \hline 1 & 5 / 18 \\
• 2 & 2 / 9 \\
• 3 & 1 / 6 \\
• 4 & 1 / 9 \\
• 5 & 1 / 18 \\
• 6 & 0
• \end{array}\)

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