Conditional Probability

/**
 * Fintech Math Bootcamp · Lesson 053 of 120
 * Conditional Probability
 * Module 06: Probability and Random Variables
 *
 * Scenario: Changing the denominator after a fraud flag
 * Rule:     P(F|A)=P(F∩A)/P(A)
 *
 * Try it:   Are P(fraud|flag) and P(flag|fraud) generally equal?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/conditional-probability/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson053() {
  const transactions=10000, flagged=500;
  const fraudAndFlagged=50, allFraud=100;
  const result = {fraudGivenFlag:fraudAndFlagged/flagged,
    flagGivenFraud:fraudAndFlagged/allFraud,
    joint:fraudAndFlagged/transactions};
  return result;
}

export const checkedResult = {"fraudGivenFlag":0.1,"flagGivenFraud":0.5,"joint":0.005};

// Run this file directly: npx tsx lessons/06-probability-and-random-variables/053-conditional-probability.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson053(), null, 2));
}

# Fintech Math Bootcamp · Lesson 053 of 120
# Conditional Probability
# Module 06: Probability and Random Variables
#
# Scenario: Changing the denominator after a fraud flag
# Rule:     P(F|A)=P(F∩A)/P(A)
#
# Try it:   Are P(fraud|flag) and P(flag|fraud) generally equal?
#
# Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/conditional-probability/
# Free course:    https://courses.thefintechbuilder.com
# Synthetic teaching example, not financial advice or a production library.

import json


def lesson053() -> dict:
    transactions, flagged = 10000, 500
    fraud_and_flagged, all_fraud = 50, 100
    return {
        "fraudGivenFlag": fraud_and_flagged / flagged,
        "flagGivenFraud": fraud_and_flagged / all_fraud,
        "joint": fraud_and_flagged / transactions,
    }


if __name__ == "__main__":
    print(json.dumps(lesson053(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 053 of 120
 * Conditional Probability
 * Module 06: Probability and Random Variables
 *
 * Scenario: Changing the denominator after a fraud flag
 * Rule:     P(F|A)=P(F∩A)/P(A)
 *
 * Try it:   Are P(fraud|flag) and P(flag|fraud) generally equal?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/conditional-probability/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

import java.util.ArrayList;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;

public class Main {
    static Map<String, Object> lesson053() {
        double transactions = 10000, flagged = 500;
        double fraudAndFlagged = 50, allFraud = 100;
        Map<String, Object> result = new LinkedHashMap<String, Object>();
        result.put("fraudGivenFlag", fraudAndFlagged / flagged);
        result.put("flagGivenFraud", fraudAndFlagged / allFraud);
        result.put("joint", fraudAndFlagged / transactions);
        return result;
    }

    public static void main(String[] args) {
        System.out.println(toJson(lesson053(), ""));
    }

    // --- Minimal JSON printer: maps keep insertion order, 2-space indent. ---

    static String toJson(Object value, String indent) {
        if (value == null) return "null";
        if (value instanceof String) return "\"" + value + "\"";
        if (value instanceof Double) return formatNumber((Double) value);
        if (value instanceof Number) return value.toString();
        if (value instanceof double[]) {
            List<Object> items = new ArrayList<Object>();
            for (double v : (double[]) value) items.add(v);
            return toJson(items, indent);
        }
        String inner = indent + "  ";
        StringBuilder sb = new StringBuilder();
        if (value instanceof Map) {
            Map<?, ?> map = (Map<?, ?>) value;
            if (map.isEmpty()) return "{}";
            sb.append("{\n");
            int i = 0;
            for (Map.Entry<?, ?> entry : map.entrySet()) {
                sb.append(inner).append('"').append(entry.getKey()).append("\": ")
                  .append(toJson(entry.getValue(), inner))
                  .append(++i < map.size() ? ",\n" : "\n");
            }
            return sb.append(indent).append('}').toString();
        }
        List<?> list = (List<?>) value;
        if (list.isEmpty()) return "[]";
        sb.append("[\n");
        for (int i = 0; i < list.size(); i++) {
            sb.append(inner).append(toJson(list.get(i), inner))
              .append(i + 1 < list.size() ? ",\n" : "\n");
        }
        return sb.append(indent).append(']').toString();
    }

    static String formatNumber(double v) {
        if (Double.isNaN(v) || Double.isInfinite(v)) return "null";
        if (v == Math.rint(v) && Math.abs(v) < 1e15) return Long.toString((long) v);
        return Double.toString(v);
    }
}

// Fintech Math Bootcamp · Lesson 053 of 120
// Conditional Probability
// Module 06: Probability and Random Variables
//
// Scenario: Changing the denominator after a fraud flag
// Rule:     P(F|A)=P(F∩A)/P(A)
//
// Try it:   Are P(fraud|flag) and P(flag|fraud) generally equal?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/conditional-probability/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

package main

import (
	"encoding/json"
	"fmt"
)

// Conditionals shows how the same joint count gives different rates per denominator.
type Conditionals struct {
	FraudGivenFlag float64 `json:"fraudGivenFlag"`
	FlagGivenFraud float64 `json:"flagGivenFraud"`
	Joint          float64 `json:"joint"`
}

func lesson053() Conditionals {
	transactions, flagged := 10000.0, 500.0
	fraudAndFlagged, allFraud := 50.0, 100.0
	return Conditionals{
		FraudGivenFlag: fraudAndFlagged / flagged,
		FlagGivenFraud: fraudAndFlagged / allFraud,
		Joint:          fraudAndFlagged / transactions,
	}
}

func main() {
	out, _ := json.MarshalIndent(lesson053(), "", "  ")
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 053 of 120
 * Conditional Probability
 * Module 06: Probability and Random Variables
 *
 * Scenario: Changing the denominator after a fraud flag
 * Rule:     P(F|A)=P(F∩A)/P(A)
 *
 * Try it:   Are P(fraud|flag) and P(flag|fraud) generally equal?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/conditional-probability/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

#include <charconv>
#include <cmath>
#include <iostream>
#include <string>
#include <utility>
#include <vector>

// --- Minimal JSON value and printer: objects keep insertion order, 2-space indent. ---

struct Json {
    enum class Kind { Null, Number, Text, Array, Object };
    Kind kind = Kind::Null;
    double number = 0;
    std::string text;
    std::vector<std::string> keys;  // object keys, parallel to items
    std::vector<Json> items;        // array elements or object values
};

Json num(double v) { Json j; j.kind = Json::Kind::Number; j.number = v; return j; }
Json str(const std::string& s) { Json j; j.kind = Json::Kind::Text; j.text = s; return j; }
Json arr(const std::vector<Json>& values) { Json j; j.kind = Json::Kind::Array; j.items = values; return j; }

Json arr(const std::vector<double>& values) {
    std::vector<Json> items;
    for (double v : values) items.push_back(num(v));
    return arr(items);
}

Json obj(const std::vector<std::pair<std::string, Json>>& fields) {
    Json j;
    j.kind = Json::Kind::Object;
    for (const auto& [key, value] : fields) { j.keys.push_back(key); j.items.push_back(value); }
    return j;
}

std::string formatNumber(double v) {
    if (!std::isfinite(v)) return "null";
    char buf[64];
    auto end = std::to_chars(buf, buf + sizeof buf, v).ptr;  // shortest round-trip form
    return std::string(buf, end);
}

void writeJson(std::ostream& out, const Json& j, const std::string& indent) {
    switch (j.kind) {
    case Json::Kind::Null: out << "null"; return;
    case Json::Kind::Number: out << formatNumber(j.number); return;
    case Json::Kind::Text: out << '"' << j.text << '"'; return;
    default: break;
    }
    bool isObject = j.kind == Json::Kind::Object;
    if (j.items.empty()) { out << (isObject ? "{}" : "[]"); return; }
    std::string inner = indent + "  ";
    out << (isObject ? "{\n" : "[\n");
    for (size_t i = 0; i < j.items.size(); ++i) {
        out << inner;
        if (isObject) out << '"' << j.keys[i] << "\": ";
        writeJson(out, j.items[i], inner);
        out << (i + 1 < j.items.size() ? ",\n" : "\n");
    }
    out << indent << (isObject ? '}' : ']');
}

// --- Lesson ---

Json lesson053() {
    const double transactions = 10000, flagged = 500;
    const double fraudAndFlagged = 50, allFraud = 100;
    return obj({
        {"fraudGivenFlag", num(fraudAndFlagged / flagged)},
        {"flagGivenFraud", num(fraudAndFlagged / allFraud)},
        {"joint", num(fraudAndFlagged / transactions)},
    });
}

int main() {
    writeJson(std::cout, lesson053(), "");
    std::cout << '\n';
}

// Fintech Math Bootcamp · Lesson 053 of 120
// Conditional Probability
// Module 06: Probability and Random Variables
//
// Scenario: Changing the denominator after a fraud flag
// Rule:     P(F|A)=P(F∩A)/P(A)
//
// Try it:   Are P(fraud|flag) and P(flag|fraud) generally equal?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/conditional-probability/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

// --- Minimal JSON value and printer: objects keep insertion order, 2-space indent. ---

#[allow(dead_code)]
enum Json {
    Null,
    Num(f64),
    Str(String),
    Arr(Vec<Json>),
    Obj(Vec<(String, Json)>),
}

#[allow(dead_code)]
fn nums(values: &[f64]) -> Json {
    Json::Arr(values.iter().map(|&v| Json::Num(v)).collect())
}

#[allow(dead_code)]
fn obj(fields: Vec<(&str, Json)>) -> Json {
    Json::Obj(fields.into_iter().map(|(k, v)| (k.to_string(), v)).collect())
}

fn format_number(v: f64) -> String {
    if !v.is_finite() {
        return "null".to_string();
    }
    if v.fract() == 0.0 && v.abs() < 1e15 {
        return format!("{}", v as i64);
    }
    format!("{:?}", v) // shortest round-trip form
}

impl Json {
    fn render(&self, indent: &str) -> String {
        let inner = format!("{}  ", indent);
        match self {
            Json::Null => "null".to_string(),
            Json::Num(v) => format_number(*v),
            Json::Str(s) => format!("\"{}\"", s),
            Json::Arr(items) if items.is_empty() => "[]".to_string(),
            Json::Obj(fields) if fields.is_empty() => "{}".to_string(),
            Json::Arr(items) => {
                let lines: Vec<String> = items.iter().map(|v| format!("{}{}", inner, v.render(&inner))).collect();
                format!("[\n{}\n{}]", lines.join(",\n"), indent)
            }
            Json::Obj(fields) => {
                let lines: Vec<String> = fields
                    .iter()
                    .map(|(k, v)| format!("{}\"{}\": {}", inner, k, v.render(&inner)))
                    .collect();
                format!("{{\n{}\n{}}}", lines.join(",\n"), indent)
            }
        }
    }
}

// --- Lesson ---

fn lesson053() -> Json {
    let (transactions, flagged) = (10000.0, 500.0);
    let (fraud_and_flagged, all_fraud) = (50.0, 100.0);
    obj(vec![
        ("fraudGivenFlag", Json::Num(fraud_and_flagged / flagged)),
        ("flagGivenFraud", Json::Num(fraud_and_flagged / all_fraud)),
        ("joint", Json::Num(fraud_and_flagged / transactions)),
    ])
}

fn main() {
    println!("{}", lesson053().render(""));
}

/**
 * Fintech Math Bootcamp · Lesson 053 of 120
 * Conditional Probability
 * Module 06: Probability and Random Variables
 *
 * Scenario: Changing the denominator after a fraud flag
 * Rule:     P(F|A)=P(F∩A)/P(A)
 *
 * Try it:   Are P(fraud|flag) and P(flag|fraud) generally equal?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/conditional-probability/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

using System;
using System.Text.Json;

var options = new JsonSerializerOptions { WriteIndented = true };
Console.WriteLine(JsonSerializer.Serialize(Lesson053(), options));

static object Lesson053()
{
    double transactions = 10000, flagged = 500;
    double fraudAndFlagged = 50, allFraud = 100;
    return new
    {
        fraudGivenFlag = fraudAndFlagged / flagged,
        flagGivenFraud = fraudAndFlagged / allFraud,
        joint = fraudAndFlagged / transactions,
    };
}