Implementing Classical Probability in R

Tossing a Coin

Let’s calculate the probability of getting heads when flipping a fair coin.

Output:

[1] 0.5

• outcomes <- c(“Heads”, “Tails”): This line creates a vector called outcomes containing two elements, “Heads” and “Tails.” These represent the possible outcomes of flipping the coin.
• total_outcomes <- length(outcomes): Here, we find the total number of possible outcomes by using the length function. In this case, there are two possible outcomes, so total_outcomes becomes 2.
• favorable_outcomes <- length(outcomes[outcomes == “Heads”]): This line counts the number of favorable outcomes, which is the number of times “Heads” appears in the outcomes vector. Since “Heads” appears once in our vector, favorable_outcomes becomes 1.
• classical_prob <- favorable_outcomes / total_outcomes: Now, we calculate the classical probability by dividing the number of favorable outcomes (which is 1) by the total number of possible outcomes (which is 2). So, classical_prob becomes 1/2, which is 0.5.
• classical_prob: Finally, we print out the value of classical_prob, which represents the probability of getting “Heads” when flipping a fair coin. In this case, it’s 0.5.

In simpler terms, this code helps us figure out the chance of getting “Heads” when we flip a coin. Since there are two possible outcomes (Heads and Tails) and only one of them is “Heads,” the probability of getting “Heads” is 1 out of 2, which is 0.5 or 50%. So, when you flip a fair coin, there’s a 50% chance it’ll land on “Heads.”

Deck of Cards

Calculating the probability of drawing a spade from a standard deck of 52 cards.

Output:

[1] 0.25

• deck <- rep(c(“Spades”, “Hearts”, “Diamonds”, “Clubs”), each = 13): Here, we create a vector called deck that represents a standard deck of playing cards. The rep function is used to repeat each of the four suits (“Spades,” “Hearts,” “Diamonds,” and “Clubs”) 13 times, which accounts for the 13 cards in each suit (Ace through 10, and the Jack, Queen, and King).
• total_cards <- length(deck): We find the total number of cards in the deck by using the length function. Since each suit has 13 cards, the total number of cards is 4 suits x 13 cards per suit, which equals 52 cards.
• spades <- length(deck[deck == “Spades”]): This line counts the number of spade cards in the deck vector. It does this by selecting all the elements in the deck vector that are equal to “Spades” and then using the length function to count them.
• classical_prob_spade <- spades / total_cards: Now, we calculate the classical probability of drawing a spade by dividing the number of spade cards (stored in the variable spades) by the total number of cards in the deck (stored in the variable total_cards).
• classical_prob_spade: Finally, we print out the value of classical_prob_spade, which represents the probability of drawing a spade from a standard deck of 52 cards.

In simpler terms, this code helps us figure out the chance of picking a spade card from a regular deck of playing cards. Since there are 52 cards in total and 13 of them are spades, the probability of drawing a spade card is 13 out of 52, which can be simplified to 1 out of 4 or 25%. So, when you draw a card from a standard deck, there’s a 25% chance it’ll be a spade.

Rolling a Die

To calculate the probability of rolling a 3 on a fair six-sided die, we can use the following formula:

There is only one favorable outcome (rolling a 3), and there are six total outcomes (rolling any number from 1 to 6). Therefore, the probability of rolling a 3 is 1/6.

We can also use R to calculate the probability. The following code defines a function called calculate_probability(), which takes the number of favorable outcomes and the total number of outcomes as arguments and returns the probability:

Output:

Probability: 0.5 
Probability: Invalid Input. Favorable outcomes must be less than or equal to the total number of outcomes 
Probability: Invalid input. Favorable outcomes must be non-negative, and the total number of outcomes must be positive. 

In this article, we delve into the fundamental concepts of classical probability within the context of the R programming language. Classical probability theory provides a solid foundation for understanding random events and their likelihood in various scenarios. We explore mathematical foundations, properties, and practical codes of classical probability, offering insights suitable for both newcomers and seasoned data analysts seeking to grasp the core principles of probability in the R environment.