Probability to consecutively extract $x$ green balls from a bag with red and green balls

Question

I am trying to figure out the formula for the following problem:

I have one bag containing n balls. m of those balls are green, and the others are red.

I am going to extract all the balls one by one and at the end I want to check whether I had groups of x or more green balls extracted consecutively.

Here is an example with numbers: if I have 28 balls, 10 green and 18 red, what's the probability that I extract 3 or more green balls consecutively (at any point of the extraction process)?

Answer 1

Hint: This is a simple example of the hypergeometric distribution. Let me know if you need more help.