# 2 HarvardX: PH125.3x Data Science: Probability

## 2.1 Section 1: Discrete Probability

### 2.1.1 Monte Carlo szimuláció

Key points -Monte Carlo simulations model the probability of different outcomes by repeating a random process a large enough number of times that the results are similar to what would be observed if the process were repeated forever.

-The sample function draws random outcomes from a set of options.

-The replicate function repeats lines of code a set number of times. It is used with sample and similar functions to run Monte Carlo simulations.

Code: The rep function and the sample function

``````beads <- rep(c("red", "blue"), times = c(2,3))    # create an urn with 2 red, 3 blue
``##  "red"  "red"  "blue" "blue" "blue"``
``sample(beads, 1)    # sample 1 bead at random``
``##  "blue"``

replicate() funkcióval eltudjuk készíteni a Monte Carlo szimulációnkat, amivel a valós eredménykhez közeli érétket kaphatunk. Tehát 10000-szer futtatva 5 db golyó közül 3 kék és 2 piros fog kijönni százalékos szinten is.

``````B <- 10000    # number of times to draw 1 bead
tab <- table(events)    # make a table of outcome counts
tab    # view count table``````
``````## events
## blue  red
## 6019 3981``````
``prop.table(tab)    # view table of outcome proportions``
``````## events
##   blue    red
## 0.6019 0.3981``````