# Topic 11 # probability is always between 0 and 1 # # demonstrate a small "catch" to this, namely # that R expresses really small, close to 0, # values in "scientific" form. For example, # look at the number 0.00000006478. 0.00000006478 # we will run 4 trials of the experiment of # getting 5 random values between 1 and 99. # Note that if you run this script then you # will get different results than are shown # here. Sort the values to make it easier to # inspect the lists. sort( as.integer( runif( 5, 1, 100)) ) sort( as.integer( runif( 5, 1, 100)) ) sort( as.integer( runif( 5, 1, 100)) ) sort( as.integer( runif( 5, 1, 100)) ) # Set up three different choices blue_hat <- c(1,2,3,4,5,6,7,8) coin <- c("H","T") fruit <- c("O","P","A","G","L") # Get thee sample space of an item # taken from each choice expand.grid( blue_hat, coin, fruit ) # look at permutations # we need to load a special package to get # the function we want. install.packages("gtools") library(gtools) # recall the values in fruit fruit # Now that we have the library installed we # can use the function permutations to get the # permutations of our 5 fruits taken 3 at a time. permutations( 5, 3, fruit ) # demonstrate factorial() factorial(8) factorial(6) # look at the surprising case factorial( 0) # find the number of permutations of 19 things # taken 4 at a time factorial( 19 ) / factorial( 19-4 ) # load all of the related functions into the # environment source("../combinations.R") # compute the answer to the previous problem # using the two functions nPr() and num_perm(). nPr( 19, 4) num_perm( 19, 4 ) # get the combinations of the 5 fruits taken # 3 at a time combinations( 5, 3, fruit) # find the number of combinations of 17 things # taken 6 at a time factorial( 17 ) /(factorial(17-6)*factorial(6)) # do this with the functions nCr and num_comb nCr( 17, 6 ) num_comb( 17, 6 )