probability_exercise.R

# Some quick R code to answer https://www.linkedin.com/posts/alexsidorenko_you-have-three-risks-a-30-probability-activity-7356011763118546944-F2ed

library(tidyverse)

stats <- tibble(cat = c("A", "B", "C"), 
                prob = c(0.3, 0.2, 0.4), 
                loss = c(100, 200, 50))

all_scenarios <- expand_grid(A = c(TRUE, FALSE),
                             B = c(TRUE, FALSE), 
                             C=c(TRUE, FALSE)) 
prob_scenarios <- all_scenarios %>% 
  mutate(scenario = row_number()) %>% 
  gather(cat, event, -scenario) %>% 
  left_join(stats, by="cat") %>% 
  mutate(true_prob = ifelse(event, prob, 1-prob),
         loss = ifelse(event, loss, 0)) %>% 
  summarize(.by=scenario, probability = prod(true_prob), loss = sum(loss)) %>% 
  mutate(txt = paste0(percent(probability), " of ", loss, "k"))

  
to_cat <- prob_scenarios %>% 
  arrange(loss) %>% 
  summarize(txt = paste0(txt, collapse=", ")) %>% 
  pull(txt)
cat(to_cat)
# 33.6% of 0k, 22.4% of 50k, 14.4% of 100k, 9.6% of 150k, 8.4% of 200k, 5.6% of 250k, 3.6% of 300k, 2.4% of 350k

exceed <- prob_scenarios %>% 
  arrange(-loss) %>% 
  mutate(cumprob = cumsum(probability)) %>% 
  mutate(txt = paste0(percent(cumprob), " of ", loss, "k or more loss"))

ggplot(exceed, aes(loss, cumprob, label=txt)) +
  geom_step(direction = "vh") +
  geom_point(size=1.5) +
  geom_text(vjust=-0.4, hjust=c(seq(1,0,length.out=nrow(exceed)))) +
  scale_x_continuous("Loss (in thousands)", expand=expansion(mult=c(0,0.06))) +
  scale_y_continuous("Probability of >= Loss", expand=expansion(mult=c(0,0.06)), limits=c(0,1))