Balls are drawn one after the other uniformly at random without replacement from a set of eight balls numbered $1,2, \ldots, 8$ until all balls drawn. What is the expected number of balls whose value match their ordinality (i.e., their position in the order in which balls were drawn)?
Hint: what is the probability that the $i$-th ball is drawn at the $i$-th draw? Now can you use linearity of expectation to solve the problem?
- $1$
- $1.5$
- $2$
- $2.5$
- None of the above