g.pr.10.3 (mc) \$p(a) = 0.25\$ and \$p(a \\cap b) = 0.175\$. a and …

QUESTION IMAGE

$g.pr.10.3 (mc) \$p(a) = 0.25\$ and \$p(a \\cap b) = 0.175\$. a and …$

Question

g.pr.10.3 (mc)

\$p(a) = 0.25\$ and \$p(a \cap b) = 0.175\$. a and b are independent events. find \$p(b)\$.

0.7
0.075
0.01875
0.25

Explanation:

Response

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Independent Events",
"Probability Formulas"
],
"new_concepts": [],
"current_concepts": [
"Independent Events",
"Probability Formulas"
]
}
</pre_analysis>

State the formula for independent events

\[
P(A \cap B) = P(A) \cdot P(B)
\]

Substitute the given values and solve for P(B)

\[

\begin{aligned} 0.175 &= 0.25 \cdot P(B) \\ P(B) &= \frac{0.175}{0.25} \\ P(B) &= 0.7 \end{aligned}

\]
</reasoning>

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

Answer: