Question

g.pr.10.6 (mc)

rachel wants to play a game at a casino where she will roll a fair die and spin a spinner with the colors red, blue, green, yellow, and orange evenly spread out. the game costs $5 to play and there are 3 ways to win.

• roll an odd number and spin red - win $5
• roll a 1 and spin blue or green - win $10
• roll a 6 and spin yellow - win $20

find the net gain of rolling an odd number and spinning red.

• +$5
• $0
• -$5
• +$1

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Net Gain"
],
"current_concepts": [
"Expected Value",
"Net Gain"
]
}
</pre_analysis>

<reasoning>

Identify the cost to play and the payout for the event

\[

$$\begin{aligned} \text{Cost to play} &= \$5 \\ \text{Payout for rolling an odd number and spinning red} &= \$5 \end{aligned}$$

\]

Calculate the net gain

\[

$$\begin{aligned} \text{Net Gain} &= \text{Payout} - \text{Cost to play} \\ \text{Net Gain} &= \$5 - \$5 \\ \text{Net Gain} &= \$0 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>+\$5</mcq-option>
<mcq-correct>\$0</mcq-correct>
<mcq-option>-\$5</mcq-option>
<mcq-option>+\$1</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Statistics",
"Expected Value"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Net Gain"
],
"current_concepts": [
"Expected Value",
"Net Gain"
]
}
</pre_analysis>

<reasoning>

Identify the cost to play and the payout for the event

\[

$$\begin{aligned} \text{Cost to play} &= \$5 \\ \text{Payout for rolling an odd number and spinning red} &= \$5 \end{aligned}$$

\]

Calculate the net gain

\[

$$\begin{aligned} \text{Net Gain} &= \text{Payout} - \text{Cost to play} \\ \text{Net Gain} &= \$5 - \$5 \\ \text{Net Gain} &= \$0 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>+\$5</mcq-option>
<mcq-correct>\$0</mcq-correct>
<mcq-option>-\$5</mcq-option>
<mcq-option>+\$1</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Statistics",
"Expected Value"
]
}
</post_analysis>