How to evaluate the probability of a range in R?

Question

Supposed I toss 10 dice many times (let's say, 10000 times), and I want to know the probability of the sum on 10 dice falling into a range (10 to 20, 20 to 30, ..., 50 to 60). How can I divide the value into range and calculate the probability of each range? Below is what I have til now:

K=10 
all_comb = rep(list(1:6),K) # set up the dice
dice <- expand.grid(all_comb) #list all possible combinations
dice.sums <- rowSums(dice) #calculate sum of each combination
all_prob = c() #calculate the probability of each possible sum (from 10 to 60)
for (i in 1:(60-10+1) ){
  a = mean( dice.sums == c(10:60)[i] ) 
  all_prob = c(all_prob,a)
}
print(all_prob)

I hope someone can tell me how to do this. Thank you very much!

To efficiently compute the full PMF, see this CV answer.

jblood94
– jblood94

2024-03-31 15:00:40 +00:00
Commented Mar 31, 2024 at 15:00 — jblood94
– jblood94, Commented Mar 31, 2024 at 15:00

Allan Cameron · Accepted Answer · 2024-03-31 12:58:35Z

3

If you create a table of dice.sums, then you will get the frequency of each possible sum. Dividing this table by its total will give you the probability of each sum. The rest is just data wrangling to get it into the correct format, for which dplyr will be useful:

library(dplyr)

table(dice.sums) %>%
  as.data.frame() %>%
  mutate(dice.sums = as.numeric(as.character(dice.sums)),
         prob = Freq/sum(Freq),
         floor = 10 * floor(dice.sums/10)) %>%
  summarise(range = paste(min(dice.sums), max(dice.sums), sep = ' - '),
            prob = round(sum(prob), 8), .by = floor) %>%
  select(range, prob)
#>     range       prob
#> 1 10 - 19 0.00148046
#> 2 20 - 29 0.15502340
#> 3 30 - 39 0.63852791
#> 4 40 - 49 0.20207825
#> 5 50 - 59 0.00288996
#> 6 60 - 60 0.00000002

answered Mar 31, 2024 at 12:58

Allan Cameron

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Comments

jay.sf · Accepted Answer · 2024-03-31 14:31:12Z

1

Perhaps you could simply do,

> n_dice <- 10
> n_toss <- 1e6
> set.seed(42)
> tss <- replicate(n_dice, sample.int(6, n_toss, replace=TRUE))
> table(cut(rowSums(tss), seq(0, 6*n_dice, 10)))/n_toss

  (0,10]  (10,20]  (20,30]  (30,40]  (40,50]  (50,60] 
0.000000 0.002883 0.202386 0.638278 0.154963 0.001490

answered Mar 31, 2024 at 14:31

jay.sf

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Comments

Edward · Accepted Answer · 2024-05-02 09:01:00Z

0

Since you're throwing dice, you can use the rmultinom function to simulate the experiment.

dice <- 10 # Number of dice
probs <- rep(1/6, 6) # probabilities for each number
n <- 100000  # simulations

set.seed(123)
samples <- rmultinom(n = n, size = dice, prob = probs)
table(cut(1:6 %*% samples, br=seq(10, 60, 10))) / n

(10,20] (20,30] (30,40] (40,50] (50,60] 
0.00257 0.20286 0.63800 0.15506 0.00151

answered May 2, 2024 at 9:01

Edward

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