I'm quite new to the whole probability branch of math, have been doing some problems, and I've come across a challenging one (in my inexperienced opinion):
There are 50 balls in an urn, 20 red, 30 white. If they are randomly being drawn without being returned, what's:
- The probability to have a white ball drawn in the 3rd draw
- The probability to have a red ball drawn in the 7th draw
- The probability to have drawn a red ball in the 7th draw if it's known that a white ball was drawn in the 3rd draw, and vice versa.
So, I've had 2 problems I just couldn't wrap my head around, and those are:
- How to calculate the probabilities for 1. and 2. I went brute force for the probability of a white ball being drawn on the 3rd draw, made a total probability tree (diagram), summed up all the good outcomes, and got $\frac35$, which would be the same as if it was being drawn in the first draw. Then I checked the same for the 2nd draw and the outcome was the same, so I could assume that the answer to question 2. would be $\frac25$, but I'm still unsure as to why, and would really appreciate an explanation to this.
- Even with those 2 solved, not quite sure how to answer question 3.
I'd be really thankful for all and any kind of explanations to these 2 problems.