This problem is about probability (and no lottery, I promise)

 

Imagine a box in which there are 6 red b***s and 4 yellow b***s. You can't see what's inside the box, and the b***s are indiscernible. The experience involves picking a ball in the box, then putting it back in the box; this experience will be repeated 3 more times (it will be performed 4 times in total).

 

Calculate the probability that :

1. the four b***s all have the same color
2. you pick exactly two red b***s and two tellow b***s (in any order)
3. you pick at least one yellow ball

Good luck!