A Fair Die Is Rolled B) C) D) E)

question 141

Multiple Choice

A fair die is rolled. Let the random variable X denote the number that falls bottommost on the die. Find the probability distribution of X.

• A) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x )& \frac { 1 } { 12 } & \frac { 1 } { 6 } &\frac { 1 } { 4 }& \frac { 1 } { 4 } &\frac { 1 } { 6} &\frac { 1 } { 12 } \\
• \end{array}\)
• B) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 }& \frac { 1 } { 3 } & \frac { 1 } { 6 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \\
• \end{array}\)
• C) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x ) &\frac { 1 } { 6 } &\frac { 1 } { 6 }& \frac { 1 } { 6 } & \frac { 1 } { 6 } & \frac { 1 } { 6} & \frac { 1 } { 6 } \\
• \end{array}\)
• D) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x ) &\frac { 1 } { 12 } &\frac { 1 } { 12 } & \frac{ 1 } { 12 } &\frac { 1 } { 12 } & \frac { 1 } { 12 } & \frac { 1 } { 12 } \\
• \end{array}\)
• E) \(\begin{array} { l }
• x & 1 & 2 & 3 & 4 & 5 & 6\\
• P ( X = x ) &\frac { 1 } { 3 } &\frac { 1 } { 3 } & \frac{ 1 } { 3 } &\frac { 1 } {3} & \frac { 1 } { 3 } & \frac { 1 } { 3 } \\
• \end{array}\)

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