2.1 Simple Probability

Interpretation:
Probability can be defined as the chance of an event occurring by calculating the number of desired outcomes with the total number of possibilities on a scale of 0 to 1, where a value of 1 means that the probability is very accurate and vice versa.

Formula:
\[P = \frac{\text{Total Number Of Favourable Outcomes}}{\text{Total Number Of Possible Outcomes}}\]

Example: Probability of drawing a Queen from a deck of cards.

# Definisikan Ruang Sampel (Total Kartu)
Total_Cards <- 52

# Definisikan Kejadian A: Mendapatkan kartu Queen (ada 4 Queen)
Favourable_Outcomes_A <- 4

# Hitung Probabilitas P(A)
P_A_Queen <- Favourable_Outcomes_A / Total_Cards

# Tampilkan Hasil
cat("Total Cards:", Total_Cards, "\n")

## Total Cards: 52

cat("Favourable Outcomes (Queen):", Favourable_Outcomes_A, "\n")

## Favourable Outcomes (Queen): 4

cat("Probability P(Queen):", round(P_A_Queen, 4), "\n")

## Probability P(Queen): 0.0769

2.2 Sample Space

Interpretation:
The Sample Space is the set of all possible outcomes of a random experiment. It defines the entire universe of possible results.

(Insert sample space Venn diagram image here if needed)

Formula (Conceptual):

Sample Space:
\[S = \{h_1, h_2, ..., h_n\}\]

Total Outcomes:
\[N = |S|\]

Note:
\(h_n\) is the n-th individual outcome, and \(|S|\) represents the total number of possible outcomes (Total Outcomes), denoted by N.

Example: Sample Space of rolling two six-sided dice.

# Ruang Sampel (S) saat melempar dua dadu (dadu 1, dadu 2)
# Setiap hasil adalah pasangan terurut (d1, d2).
# Total kemungkinan hasil: 6 * 6 = 36

Total_Outcomes_N_Dice <- 6 * 6

# Contoh beberapa hasil dalam ruang sampel S
Example_Outcomes <- c("(1, 1)", "(1, 2)", "(2, 1)", "(6, 6)")

# Tampilkan hasil
cat("Example Outcomes in S:", Example_Outcomes, "\n")

## Example Outcomes in S: (1, 1) (1, 2) (2, 1) (6, 6)

cat("Total Outcomes (N) for Two Dice:", Total_Outcomes_N_Dice, "\n")

## Total Outcomes (N) for Two Dice: 36

2.3 Complement Rule

Interpretation:
The Complement Rule states that the probability of an event not happening is equal to1 minus the probability of the event happening.
The complement of event A is written as A′ (A prime) or Aᶜ.

This rule is useful when calculating probabilities of events that are easier to evaluate by first determining what does not occur.

Formula:
\[ P(A') = 1 - P(A) \]

Example: Probability of not drawing a Queen from a standard deck of 52 cards.

# Probabilitas menggunakan Aturan Komplemen (Complement Rule)

# Probabilitas mendapatkan Queen (ada 4 Queen dari 52 kartu)
P_Queen <- 4 / 52  

# Aturan komplemen: probabilitas TIDAK mendapatkan Queen
P_Not_Queen <- 1 - P_Queen  

# Tampilkan hasil
cat("P(Queen):", round(P_Queen, 4), "\n")             # Menampilkan peluang mendapatkan Queen

## P(Queen): 0.0769

cat("P(Not Queen):", round(P_Not_Queen, 4), "\n")     # Menampilkan peluang tidak mendapatkan Queen

## P(Not Queen): 0.9231