solutions/Mission409Solutions.Rmd

---
title: "Probability Fundamentals in R: Guided Project Solutions"
output: html_document
---

# Developing A Mobile App For Alleviating Lottery Addiction

This RMarkdown file is intended to lay out the logic of a mobile app designed for those addicted to the lottery. By showing a user how to calculate the incredibly small probabilities of winning the lottery, we hope that the app will help them better grasp that buying multiple lottery tickets will do little to help them win. Through this understanding, they will hopefully stop purchasing lottery tickets in an unhealthy manner.

# Core Functions

```{r}
factorial <- function(n) {
  product = 1
  for (i in 1:n) {
    product = product * i
  }
  return(product)
}

combinations <- function(n, k) {
  numerator <- factorial(n)
  denominator <- factorial(k) * factorial(n - k)
  return(numerator / denominator)
}
```

# One-Ticket Probability

```{r}
one_ticket_probability <- function(nums) {
  total_combinations <- combinations(49, 6)
  prob <- (1 / total_combinations) * 100
  pretty_prob <- sprintf("%1.9f", prob)
  s <- paste("You have a ", pretty_prob, "% chance of winning the big prize.", sep = "")
  return(s)
}

one_ticket_probability(c(1, 2, 3, 4, 5, 6))
```

# Historical Data Check for Canada Lottery

```{r, message = FALSE, warning = FALSE}
library(tidyverse)
lottery649 <- read_csv("649.csv")

print(dim(lottery649))
```

```{r}
head(lottery649, 3)
```

```{r}
tail(lottery649, 3)
```

# A New Data Structure

```{r}
data1 <- c(1, 3, 5)
data2 <- c(2, 4, 6)
data3 <- c(8, 9, 7)

## Answer
unnamed_list <- list(data1, data2, data3)
first_vector <- unnamed_list[[1]]
named_list <-list(first = data1, second = data2, third = data3)
first_item_sum <- named_list$data1[1] + named_list$data2[1] + named_list$data3[1]
```

# Using pmap

```{r}
data1 <- c(1, 3, 5)
data2 <- c(2, 4, 6)
data3 <- c(8, 9, 7)
data_list <- list(data1, data2, data3)

## Answer
averages <- pmap(data_list, function(x, y, z) { (x + y + z) / 3 })
first_average <- unlist(averages)[1]
```


# Function for Historical Data Check

```{r}
historical_lots <- pmap(
  list(
    u <- lottery649$`NUMBER DRAWN 1`,
    v <- lottery649$`NUMBER DRAWN 2`,
    w <- lottery649$`NUMBER DRAWN 3`,
    x <- lottery649$`NUMBER DRAWN 4`,
    y <- lottery649$`NUMBER DRAWN 5`,
    z <- lottery649$`NUMBER DRAWN 6`
  ), 
  .f <- function(u, v, w, x, y, z) { c(u, v, w, x, y, z) }
  )
```

```{r}
library(sets)
check_historical_occurrences <- function(lot, hist_lots = historical_lots) {
  historical_matches <- map(hist_lots, function(x) {setequal(x, lot)})
  num_past_matches <- sum(unlist(historical_matches))
  s <- paste("The combination you entered has appeared ", 
             num_past_matches, 
             " times in the past. ",
             "Your chance of winning the big prize in the next drawing using this combination is 0.0000072%", sep = "")
  return(s)
}

check_historical_occurrences(c(3, 12, 11, 14, 41, 43))
check_historical_occurrences(c(1, 2, 3, 4, 5, 6))
```

# Multi-ticket Probability

```{r}
multi_ticket_probability <- function(n) {
  total_combinations <- combinations(49, 6)
  prob <- (n / total_combinations) * 100
  pretty_prob <- sprintf("%1.9f", prob)
  s <- paste("you have a ", pretty_prob, "% chance of winning the big prize.", sep = "")
  return(s)
}
```

```{r}
test_amounts <- c(1, 10, 100, 10000, 1000000, 6991908, 13983816)
for (n in test_amounts) {
  print(paste("For ", n, " tickets, ",  multi_ticket_probability(n), sep = ""))
}
```

# Less Winning Numbers

```{r}
probability_less_6 <- function(n) {
  
    n_combinations_ticket = combinations(6, n)
    n_combinations_remaining = combinations(43, 6 - n)
    successful_outcomes = n_combinations_ticket * n_combinations_remaining
    n_combinations_total = combinations(49, 6)
    
    prob = (successful_outcomes / n_combinations_total) * 100
    pretty_prob <- sprintf("%1.9f", prob)
  
  s <- paste("you have a ", pretty_prob, "% chance of winning the big prize.", sep = "")
  return(s)
}
```

```{r}
winning_nums <- c(3, 4, 5)
for (n in winning_nums) {
  print(paste("For ", n, " tickets, ",  probability_less_6(n), sep = ""))
}
```