You Roll a Fair Die B) C) D) E) $$\begin{array} { l | c c } \text { Amount won } & \$ 70 & \$ 30 \\\hline \text { P(Amount won) } & \frac { 2 } { 6 } & \frac { 4 } { 6 }\end{array}$$

question 19

Multiple Choice

You roll a fair die.If you get a number greater than 4,you win $70.If not,you get to roll again.If you get a number greater than 4 the second time,you win $30.Otherwise you win nothing. Create a probability model for the amount you win at this game.

• A) \[\begin{array} { l | c c c }
• \text { Amount won } & \$ 70 & \$ 30 & \$ 0 \\
• \hline \text { P(Amount won) } & \frac { 2 } { 6 } & \frac { 8 } { 36 } & \frac { 16 } { 36 }
• \end{array}\]
• B) \[\begin{array} { l | c c c c }
• \text { Amount won } & \$ 100 & \$ 70 & \$ 30 & \$ 0 \\
• \hline \mathrm { P } \text { (Amount won) } & \frac { 4 } { 36 } & \frac { 8 } { 36 } & \frac { 8 } { 36 } & \frac { 16 } { 36 }
• \end{array}\]
• C) \[\begin{array} { l | c c c }
• \text { Amount won } & \$ 70 & \$ 30 & \$ 0 \\
• \hline \mathrm { P } \text { (Amount won) } & \frac { 2 } { 6 } & \frac { 2 } { 6 } & \frac { 2 } { 6 }
• \end{array}\]
• D) \[\begin{array} { l | c c c c }
• \text { Amount won } & \$ 100 & \$ 70 & \$ 30 & \$ 0 \\
• \hline \mathrm { P } \text { (Amount won) } & \frac { 4 } { 36 } & \frac { 2 } { 36 } & \frac { 2 } { 36 } & \frac { 16 } { 36 }
• \end{array}\]
• E) \[\begin{array} { l | c c }
• \text { Amount won } & \$ 70 & \$ 30 \\
• \hline \text { P(Amount won) } & \frac { 2 } { 6 } & \frac { 4 } { 6 }
• \end{array}\]

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Definitions:

Underextension

Restricting the use of a word to only a few, rather than to all, members of a class of objects.

Operant Conditioning

A process of instruction that modifies behavior strength by employing incentives or disincentives.

Zone of Proximal Development

A concept in educational psychology referring to the difference between what a learner can do without help and what they can achieve with guidance and encouragement from a skilled partner.

Scaffolding

An educational technique that involves providing support to students or learners in the early stages of learning, gradually removing the support as the learner becomes more proficient.