Update explainers/explainer_probability.py

explainers/explainer_probability.py

@@ -2,10 +2,9 @@ import re
 from .explainer_types import ExplainerResult, ExplainerScaffold
 
 
-def explain_probability_question(text: str) -> ExplainerResult | None:
-    t = text.lower()
+def explain_probability_question(text: str):
+    low = (text or "").lower()
 
-    # ✅ STRONG detection
     probability_signals = [
         "probability",
         "chance",
@@ -19,64 +18,103 @@ def explain_probability_question(text: str) -> ExplainerResult | None:
         "with replacement",
     ]
 
-    has_probability = any(p in t for p in probability_signals)
-
-    if not has_probability:
+    if not any(signal in low for signal in probability_signals):
         return None
 
-    givens = []
-    relationships = []
-    constraints = []
-    trap_notes = []
-
-    numbers = re.findall(r"\b\d+\b", t)
+    subtype = "dependent_events" if "without replacement" in low else "independent_events" if "with replacement" in low else "general_probability"
 
+    result = ExplainerResult(
+        understood=True,
+        topic="probability",
+        summary="This is a probability problem. The goal is to compare favorable outcomes to total possible outcomes.",
+        asks_for="the probability of a specific event or combination of events",
+        plain_english="Probability questions become much easier once you define exactly what counts as success and what the full sample space is.",
+    )
+
+    scaffold = ExplainerScaffold(
+        concept="Probability compares favorable outcomes to total outcomes.",
+        ask="Identify what counts as a successful outcome and what the total possible outcomes are.",
+        target="Set up favorable ÷ total before calculating.",
+        answer_hidden=True,
+        solution_path_type=subtype,
+    )
+
+    numbers = re.findall(r"\b\d+\b", low)
     if numbers:
-        givens.append(f"Numbers mentioned: {', '.join(numbers[:5])}")
+        result.givens.append(f"Numbers mentioned: {', '.join(numbers[:5])}")
     else:
-        givens.append("A situation involving possible outcomes is described")
+        result.givens.append("A situation involving possible outcomes is described.")
 
-    if "without replacement" in t:
-        relationships.append("The probabilities change after each selection")
-        constraints.append("The total number of items decreases after each draw")
-
-    if "with replacement" in t:
-        relationships.append("The probabilities stay the same for each selection")
+    result.relationships = [
+        "Probability = favorable outcomes ÷ total possible outcomes",
+    ]
+    result.needed_concepts = [
+        "favorable vs total outcomes",
+        "independent vs dependent events",
+        "complement rule",
+    ]
+    result.trap_notes = [
+        "Make sure you correctly identify the total number of possible outcomes.",
+        "Check whether events are independent or dependent.",
+        "Watch for 'at least' — often easier to use the complement.",
+        "Be careful not to double count outcomes.",
+    ]
+    result.strategy_hint = "Start by identifying all possible outcomes, then count how many satisfy the condition."
 
-    if "at least" in t:
-        relationships.append("This may require using the complement (1 - probability of the opposite event)")
+    if "without replacement" in low:
+        result.constraints.append("The total number of items decreases after each draw.")
+        result.relationships.append("The probabilities change after each selection.")
 
-    if "both" in t or "and" in t:
-        relationships.append("You may need to combine probabilities of multiple events occurring together")
+    if "with replacement" in low:
+        result.relationships.append("The probabilities stay the same for each selection.")
 
-    if "or" in t:
-        relationships.append("You may need to consider multiple possible favorable cases")
+    if "at least" in low:
+        result.relationships.append("This may be easier through the complement: 1 − probability of the opposite event.")
 
-    # default structure
-    relationships.append("Probability = favorable outcomes ÷ total possible outcomes")
+    if "both" in low or "and" in low:
+        result.relationships.append("You may need to combine probabilities of multiple events occurring together.")
 
-    asks_for = "the probability of a specific event occurring"
+    if "or" in low:
+        result.relationships.append("You may need to consider multiple favorable cases without double counting.")
 
-    trap_notes.extend([
-        "Make sure you correctly identify the total number of possible outcomes",
-        "Check whether events are independent or dependent",
-        "Watch for 'at least' — often easier to use the complement",
-        "Be careful not to double count outcomes",
-    ])
+    scaffold.setup_actions = [
+        "Define what counts as a favorable outcome.",
+        "Count or describe the total possible outcomes.",
+        "Check whether the events are independent or dependent.",
+    ]
+    scaffold.intermediate_steps = [
+        "If multiple events occur together, decide whether to multiply or add probabilities.",
+        "If the wording says 'at least', consider using the complement.",
+        "Check whether order matters.",
+    ]
+    scaffold.first_move = "Start by identifying the total number of outcomes."
+    scaffold.next_hint = "Then count how many outcomes match the condition."
+    scaffold.common_traps = [
+        "Forgetting the total outcomes.",
+        "Mixing up 'and' vs 'or'.",
+        "Ignoring replacement vs no replacement.",
+    ]
+    scaffold.key_operations = [
+        "count the sample space",
+        "count favorable cases",
+        "choose multiply/add/complement appropriately",
+    ]
+    scaffold.hint_ladder = [
+        "What counts as success here?",
+        "What is the full sample space?",
+        "Do you need multiplication, addition, or the complement rule?",
+    ]
 
-    return ExplainerResult(
-        understood=True,
-        topic="probability",
-        asks_for=asks_for,
-        givens=givens,
-        constraints=constraints,
-        relationships=relationships,
-        needed_concepts=[
-            "favorable vs total outcomes",
-            "independent vs dependent events",
-            "complement rule",
-        ],
-        trap_notes=trap_notes,
-        strategy_hint="Start by identifying all possible outcomes, then count how many satisfy the condition.",
-        plain_english="The question is asking you to work out how likely an event is by comparing favorable outcomes to all possible outcomes.",
-    )
+    result.teaching_points = [
+        "Probability = favorable / total.",
+        "Use multiplication for linked 'and' events when appropriate.",
+        "Use the complement when 'at least' is easier to solve indirectly.",
+    ]
+    result.scaffold = scaffold
+    result.meta = {
+        "intent": "explain_question",
+        "bridge_ready": True,
+        "hint_style": "step_ready",
+        "subtype": subtype,
+    }
+    return result