Topic: Probability

Probability - probability: the likelihood an event will occur (given as a number from 0 to 1: 0 being impossible and 1 being guaranteed)

Addition Rule P(A∪B)=P(A)+P(B)-P(A∩B)

Multiplication Rule P(A∩B)=P(A)*P(B)

Conditional Probability \[ P(A|B) = \frac{P(A\cap B)}{P(B)} \]

Coin Toss Simulation

set.seed(15)
coin_toss <- sample(c("heads", "tails"), size = 150, replace = TRUE)
probability_heads <- sum(coin_toss == "heads") / length(coin_toss)
probability_heads

## [1] 0.5733333

Coin Toss Simulation: Graph 1

## [1] 0.5733333

Coin Toss Simulation: Graph 2

## [1] 0.5066667

## Probability Distribution

Binomial Distribution \[ P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} \] - \(n\) number of trials, - \(k\) number of successes, - \(p\) number probability of success for each trial