Describe the Sample Space S of the Experiment and List

question 7

Multiple Choice

Describe the sample space S of the experiment and list the elements of the given event E.
Two indistinguishable dice are rolled; both numbers are composite.

• A) S = \(\left\{\begin{array} { r }
• ( ( 1,2 ) ( 1,2 ) ( 1,3 ) ( 1,4 ) ( 1,5 ) ( 1,6 ) \\
• ( 2,2 ) ( 2,3 ) ( 2,4 ) ( 2,5 ) ( 2,6 ) \\
• ( 3,3 ) ( 3,4 ) ( 3,5 ) ( 3,6 ) \\
• ( 4,4 ) ( 4,5 ) ( 4,6 ) \\
• \begin{array} { r }
• ( 5,5 ) ( 5,6 ) \\
• ( 6,6 )
• \end{array} \\
• \end{array}\right\}\)
• E = \(\{ ( 4,4 ) , ( 4,6 ) , ( 6,6 ) \}\)
• B) S = \(\left\{\begin{array}{l}
• (1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\
• (2,1)(2,2)(2,3)(2,4)(2,5)(2,6) \\
• (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\
• (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\
• (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\
• (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
• \end{array}\right\}\)
• \(E = \{ ( 2,2 ) , ( 2,4 ) , ( 2,6 ) , ( 4,4 ) , ( 4,6 ) , ( 6,6 ) \}\)
• C) S = \(\left\{\begin{array} { r }
• ( ( 1,1 ) ( 1,2 ) ( 1,3 ) ( 1,4 ) ( 1,5 ) ( 1,6 ) \\
• ( 2,2 ) ( 2,3 ) ( 2,4 ) ( 2,5 ) ( 2,6 ) \\
• ( 3,3 ) ( 3,4 ) ( 3,5 ) ( 3,6 ) \\
• ( 4,4 ) ( 4,5 ) ( 4,6 ) \\
• ( 5,5 ) ( 5,6 ) \\
• ( 6,6 )
• \end{array}\right\}\)

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Definitions:

Directional Alternative Hypothesis

A type of alternative hypothesis that specifies the direction of the anticipated difference or effect between groups or variables.

Null Hypothesis

A hypothesis that assumes no significant difference or effect between the variables being studied, serving as a default position.

Alternative Hypothesis

A theory that contradicts the null hypothesis and proposes that there is a statistically significant effect or difference.

Hybrid Cars

Vehicles that use a combination of an internal combustion engine and one or more electric motors for propulsion.