library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union#outcome for each die roll
d_1 <- c(1,2,3,4,5,6)
d_2 <- c(1,2,3,4,5,6)
d_3 <- c(1,2,3,4,5,6)
#make a df for all combinations
df <- expand.grid(d_1, d_2, d_3)
#sum into the sum of each roll
df$sum_of_rolls <- rowSums(df)
#probability is identical for each roll, 1 out of 6^3
df$roll_prob <- 1/(6^3)
#create a conditional column for greater than 9
df$greater_than_9 <- ifelse(df$sum_of_rolls > 9, "YES", "NO")
#create a conditional column for odd
df$odd <- ifelse(df$sum_of_rolls %% 2 == 1, "YES", "NO")Greater than 9:
df %>%
group_by(greater_than_9) %>%
summarise(sum(roll_prob))## # A tibble: 2 × 2
## greater_than_9 `sum(roll_prob)`
## <chr> <dbl>
## 1 NO 0.375
## 2 YES 0.625Odd:
df %>%
group_by(odd) %>%
summarise(sum(roll_prob))## # A tibble: 2 × 2
## odd `sum(roll_prob)`
## <chr> <dbl>
## 1 NO 0.500
## 2 YES 0.500df## Var1 Var2 Var3 sum_of_rolls roll_prob greater_than_9 odd
## 1 1 1 1 3 0.00462963 NO YES
## 2 2 1 1 4 0.00462963 NO NO
## 3 3 1 1 5 0.00462963 NO YES
## 4 4 1 1 6 0.00462963 NO NO
## 5 5 1 1 7 0.00462963 NO YES
## 6 6 1 1 8 0.00462963 NO NO
## 7 1 2 1 4 0.00462963 NO NO
## 8 2 2 1 5 0.00462963 NO YES
## 9 3 2 1 6 0.00462963 NO NO
## 10 4 2 1 7 0.00462963 NO YES
## 11 5 2 1 8 0.00462963 NO NO
## 12 6 2 1 9 0.00462963 NO YES
## 13 1 3 1 5 0.00462963 NO YES
## 14 2 3 1 6 0.00462963 NO NO
## 15 3 3 1 7 0.00462963 NO YES
## 16 4 3 1 8 0.00462963 NO NO
## 17 5 3 1 9 0.00462963 NO YES
## 18 6 3 1 10 0.00462963 YES NO
## 19 1 4 1 6 0.00462963 NO NO
## 20 2 4 1 7 0.00462963 NO YES
## 21 3 4 1 8 0.00462963 NO NO
## 22 4 4 1 9 0.00462963 NO YES
## 23 5 4 1 10 0.00462963 YES NO
## 24 6 4 1 11 0.00462963 YES YES
## 25 1 5 1 7 0.00462963 NO YES
## 26 2 5 1 8 0.00462963 NO NO
## 27 3 5 1 9 0.00462963 NO YES
## 28 4 5 1 10 0.00462963 YES NO
## 29 5 5 1 11 0.00462963 YES YES
## 30 6 5 1 12 0.00462963 YES NO
## 31 1 6 1 8 0.00462963 NO NO
## 32 2 6 1 9 0.00462963 NO YES
## 33 3 6 1 10 0.00462963 YES NO
## 34 4 6 1 11 0.00462963 YES YES
## 35 5 6 1 12 0.00462963 YES NO
## 36 6 6 1 13 0.00462963 YES YES
## 37 1 1 2 4 0.00462963 NO NO
## 38 2 1 2 5 0.00462963 NO YES
## 39 3 1 2 6 0.00462963 NO NO
## 40 4 1 2 7 0.00462963 NO YES
## 41 5 1 2 8 0.00462963 NO NO
## 42 6 1 2 9 0.00462963 NO YES
## 43 1 2 2 5 0.00462963 NO YES
## 44 2 2 2 6 0.00462963 NO NO
## 45 3 2 2 7 0.00462963 NO YES
## 46 4 2 2 8 0.00462963 NO NO
## 47 5 2 2 9 0.00462963 NO YES
## 48 6 2 2 10 0.00462963 YES NO
## 49 1 3 2 6 0.00462963 NO NO
## 50 2 3 2 7 0.00462963 NO YES
## 51 3 3 2 8 0.00462963 NO NO
## 52 4 3 2 9 0.00462963 NO YES
## 53 5 3 2 10 0.00462963 YES NO
## 54 6 3 2 11 0.00462963 YES YES
## 55 1 4 2 7 0.00462963 NO YES
## 56 2 4 2 8 0.00462963 NO NO
## 57 3 4 2 9 0.00462963 NO YES
## 58 4 4 2 10 0.00462963 YES NO
## 59 5 4 2 11 0.00462963 YES YES
## 60 6 4 2 12 0.00462963 YES NO
## 61 1 5 2 8 0.00462963 NO NO
## 62 2 5 2 9 0.00462963 NO YES
## 63 3 5 2 10 0.00462963 YES NO
## 64 4 5 2 11 0.00462963 YES YES
## 65 5 5 2 12 0.00462963 YES NO
## 66 6 5 2 13 0.00462963 YES YES
## 67 1 6 2 9 0.00462963 NO YES
## 68 2 6 2 10 0.00462963 YES NO
## 69 3 6 2 11 0.00462963 YES YES
## 70 4 6 2 12 0.00462963 YES NO
## 71 5 6 2 13 0.00462963 YES YES
## 72 6 6 2 14 0.00462963 YES NO
## 73 1 1 3 5 0.00462963 NO YES
## 74 2 1 3 6 0.00462963 NO NO
## 75 3 1 3 7 0.00462963 NO YES
## 76 4 1 3 8 0.00462963 NO NO
## 77 5 1 3 9 0.00462963 NO YES
## 78 6 1 3 10 0.00462963 YES NO
## 79 1 2 3 6 0.00462963 NO NO
## 80 2 2 3 7 0.00462963 NO YES
## 81 3 2 3 8 0.00462963 NO NO
## 82 4 2 3 9 0.00462963 NO YES
## 83 5 2 3 10 0.00462963 YES NO
## 84 6 2 3 11 0.00462963 YES YES
## 85 1 3 3 7 0.00462963 NO YES
## 86 2 3 3 8 0.00462963 NO NO
## 87 3 3 3 9 0.00462963 NO YES
## 88 4 3 3 10 0.00462963 YES NO
## 89 5 3 3 11 0.00462963 YES YES
## 90 6 3 3 12 0.00462963 YES NO
## 91 1 4 3 8 0.00462963 NO NO
## 92 2 4 3 9 0.00462963 NO YES
## 93 3 4 3 10 0.00462963 YES NO
## 94 4 4 3 11 0.00462963 YES YES
## 95 5 4 3 12 0.00462963 YES NO
## 96 6 4 3 13 0.00462963 YES YES
## 97 1 5 3 9 0.00462963 NO YES
## 98 2 5 3 10 0.00462963 YES NO
## 99 3 5 3 11 0.00462963 YES YES
## 100 4 5 3 12 0.00462963 YES NO
## 101 5 5 3 13 0.00462963 YES YES
## 102 6 5 3 14 0.00462963 YES NO
## 103 1 6 3 10 0.00462963 YES NO
## 104 2 6 3 11 0.00462963 YES YES
## 105 3 6 3 12 0.00462963 YES NO
## 106 4 6 3 13 0.00462963 YES YES
## 107 5 6 3 14 0.00462963 YES NO
## 108 6 6 3 15 0.00462963 YES YES
## 109 1 1 4 6 0.00462963 NO NO
## 110 2 1 4 7 0.00462963 NO YES
## 111 3 1 4 8 0.00462963 NO NO
## 112 4 1 4 9 0.00462963 NO YES
## 113 5 1 4 10 0.00462963 YES NO
## 114 6 1 4 11 0.00462963 YES YES
## 115 1 2 4 7 0.00462963 NO YES
## 116 2 2 4 8 0.00462963 NO NO
## 117 3 2 4 9 0.00462963 NO YES
## 118 4 2 4 10 0.00462963 YES NO
## 119 5 2 4 11 0.00462963 YES YES
## 120 6 2 4 12 0.00462963 YES NO
## 121 1 3 4 8 0.00462963 NO NO
## 122 2 3 4 9 0.00462963 NO YES
## 123 3 3 4 10 0.00462963 YES NO
## 124 4 3 4 11 0.00462963 YES YES
## 125 5 3 4 12 0.00462963 YES NO
## 126 6 3 4 13 0.00462963 YES YES
## 127 1 4 4 9 0.00462963 NO YES
## 128 2 4 4 10 0.00462963 YES NO
## 129 3 4 4 11 0.00462963 YES YES
## 130 4 4 4 12 0.00462963 YES NO
## 131 5 4 4 13 0.00462963 YES YES
## 132 6 4 4 14 0.00462963 YES NO
## 133 1 5 4 10 0.00462963 YES NO
## 134 2 5 4 11 0.00462963 YES YES
## 135 3 5 4 12 0.00462963 YES NO
## 136 4 5 4 13 0.00462963 YES YES
## 137 5 5 4 14 0.00462963 YES NO
## 138 6 5 4 15 0.00462963 YES YES
## 139 1 6 4 11 0.00462963 YES YES
## 140 2 6 4 12 0.00462963 YES NO
## 141 3 6 4 13 0.00462963 YES YES
## 142 4 6 4 14 0.00462963 YES NO
## 143 5 6 4 15 0.00462963 YES YES
## 144 6 6 4 16 0.00462963 YES NO
## 145 1 1 5 7 0.00462963 NO YES
## 146 2 1 5 8 0.00462963 NO NO
## 147 3 1 5 9 0.00462963 NO YES
## 148 4 1 5 10 0.00462963 YES NO
## 149 5 1 5 11 0.00462963 YES YES
## 150 6 1 5 12 0.00462963 YES NO
## 151 1 2 5 8 0.00462963 NO NO
## 152 2 2 5 9 0.00462963 NO YES
## 153 3 2 5 10 0.00462963 YES NO
## 154 4 2 5 11 0.00462963 YES YES
## 155 5 2 5 12 0.00462963 YES NO
## 156 6 2 5 13 0.00462963 YES YES
## 157 1 3 5 9 0.00462963 NO YES
## 158 2 3 5 10 0.00462963 YES NO
## 159 3 3 5 11 0.00462963 YES YES
## 160 4 3 5 12 0.00462963 YES NO
## 161 5 3 5 13 0.00462963 YES YES
## 162 6 3 5 14 0.00462963 YES NO
## 163 1 4 5 10 0.00462963 YES NO
## 164 2 4 5 11 0.00462963 YES YES
## 165 3 4 5 12 0.00462963 YES NO
## 166 4 4 5 13 0.00462963 YES YES
## 167 5 4 5 14 0.00462963 YES NO
## 168 6 4 5 15 0.00462963 YES YES
## 169 1 5 5 11 0.00462963 YES YES
## 170 2 5 5 12 0.00462963 YES NO
## 171 3 5 5 13 0.00462963 YES YES
## 172 4 5 5 14 0.00462963 YES NO
## 173 5 5 5 15 0.00462963 YES YES
## 174 6 5 5 16 0.00462963 YES NO
## 175 1 6 5 12 0.00462963 YES NO
## 176 2 6 5 13 0.00462963 YES YES
## 177 3 6 5 14 0.00462963 YES NO
## 178 4 6 5 15 0.00462963 YES YES
## 179 5 6 5 16 0.00462963 YES NO
## 180 6 6 5 17 0.00462963 YES YES
## 181 1 1 6 8 0.00462963 NO NO
## 182 2 1 6 9 0.00462963 NO YES
## 183 3 1 6 10 0.00462963 YES NO
## 184 4 1 6 11 0.00462963 YES YES
## 185 5 1 6 12 0.00462963 YES NO
## 186 6 1 6 13 0.00462963 YES YES
## 187 1 2 6 9 0.00462963 NO YES
## 188 2 2 6 10 0.00462963 YES NO
## 189 3 2 6 11 0.00462963 YES YES
## 190 4 2 6 12 0.00462963 YES NO
## 191 5 2 6 13 0.00462963 YES YES
## 192 6 2 6 14 0.00462963 YES NO
## 193 1 3 6 10 0.00462963 YES NO
## 194 2 3 6 11 0.00462963 YES YES
## 195 3 3 6 12 0.00462963 YES NO
## 196 4 3 6 13 0.00462963 YES YES
## 197 5 3 6 14 0.00462963 YES NO
## 198 6 3 6 15 0.00462963 YES YES
## 199 1 4 6 11 0.00462963 YES YES
## 200 2 4 6 12 0.00462963 YES NO
## 201 3 4 6 13 0.00462963 YES YES
## 202 4 4 6 14 0.00462963 YES NO
## 203 5 4 6 15 0.00462963 YES YES
## 204 6 4 6 16 0.00462963 YES NO
## 205 1 5 6 12 0.00462963 YES NO
## 206 2 5 6 13 0.00462963 YES YES
## 207 3 5 6 14 0.00462963 YES NO
## 208 4 5 6 15 0.00462963 YES YES
## 209 5 5 6 16 0.00462963 YES NO
## 210 6 5 6 17 0.00462963 YES YES
## 211 1 6 6 13 0.00462963 YES YES
## 212 2 6 6 14 0.00462963 YES NO
## 213 3 6 6 15 0.00462963 YES YES
## 214 4 6 6 16 0.00462963 YES NO
## 215 5 6 6 17 0.00462963 YES YES
## 216 6 6 6 18 0.00462963 YES NO