Obtain the Probability Distribution of the Random Variable $(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)$

question 121

Multiple Choice

Obtain the probability distribution of the random variable.
-When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below. $(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)$
$(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)$
$(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)$
$(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)$
$(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)$
$(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)$

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

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