Solved.
I mean that I solved it. The problem is in the Math Challenge subforum instead of Pre-University Algebra. People who post here often know the answer to their problem, think that the problem is worth solving and want to offer a challenge to others. I thought I would let people know that the problem is solvable without taking away the opportunity to meet the challenge.
If, on the other hand, you need help with the problem, then you were supposed to describe your attempts and the difficulty you are having. Have you solved any word problems that lead to a system of equations before? If not, then you should read how to do this before trying to solve a concrete problem.
I just did not understand what the word "Probability" in the thread title has to do with the problem.
The "probability" is that the original poster had no idea what the problem was asking. After all, getting someone else to do your homework for you is much easier than thinking about it.
In any case, if we make the reasonable assumption that the number of roses of each kind is an integer, this situation is impossible.
"There are a total of 149 yellow,red,white roses."
Let x, y, z be the number of yellow, red, and white roses respectively.
Then x+ y+ z= 149.
"There are 4 times as many yellow roses as red roses "
So x= 4y which is equivalent to y= x/4
"and 13 more yellow roses than white roses."
so x= z+ 13 which is equivalent to z= x- 13.
Replacing y and z with those, x+ (1/4)x+ x- 13= 149 gives (9/4)x= 162, x= (4/9)(162) but since 162 is NOT divisible by 9, that is not an integer.