There are 10 balls in a box, each has same probability of being black or being white, i.e., $P[x_i=Black]=P[x_i=White]=0.5$ for $i=1 \to 10$. Every time a ball is picked at random, it is then returned back to the box.
Compute the following:
- The probability of only white balls in the box if no black ball appears in the first four picks.
- The probability that at least two black balls are in the box if we pick exactly one black ball in first four picks.
- The distribution of black balls in the box if we pick only white balls on the first ten picks.
I cannot understand how "putting a ball back in the box after ball is picked" express in a formula.