\(P(O=52)\)

You have an 8-sided die with 4 faces colored orange, 3 colored red, and 1 colored yellow. You're going to roll the die 100 times: Let \(Y\) be the number of times a yellow face is showing, \(R\) be the number of times a red face is showing, and \(O\) be the number of times an orange face is showing. Find the given probabilities, rounded to 4 decimal places.