---
title: "Session 9 — Probability as frequency"
subtitle: "QSS 6.1 | Probability and Statistics (MIR)"
author: "Prof. Dae-Jin Lee (daelee@faculty.ie.edu)"
date: "Fall 2026"
output:
  html_document:
    toc: true
    toc_float: true
    theme: flatly
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
library(tidyverse)
```

Treat the survey as a teaching population. Estimate probabilities as shares.

```{r}
survey <- read_csv("data/survey_attitudes.csv")
glimpse(survey)
```

# Event: high support for international cooperation

```{r}
survey <- survey |>
  mutate(high_support = support_international_cooperation >= 7)

mean(survey$high_support)
```

**Interpret:** the share with score ≥ 7 estimates $P(\text{high support})$ in this population.

# Another event: high perceived threat

```{r}
survey <- survey |>
  mutate(high_threat = perceived_security_threat >= 6)

mean(survey$high_threat)
```

# Joint share (intersection)

```{r}
mean(survey$high_support & survey$high_threat)
```

Compare later to the product of the two means if you want a quick independence check.