Random Variables: from another perspective, the problem may be different.

 

 This conclusion is very important. For example, in the next question, there are n boxes and N balls. Put N balls in N boxes, the expected number of empty boxes is required. The analysis is as follows:

1,We do not want to select a box randomly. If we randomly put a ball into one of the N boxes, the probability that the ball is not in the selected box is 1-1/N (in fact, it is a drawing model ). If we regard the ball as an independent event for n times, after the ball is put for n times, the probability that the box is still empty is POW (1-1/N, N ).

 

2,For a box randomly selected, it is null and expected to be pow (1-1/n, n), it is determined by the expected formula above, the number of empty boxes is expected to be n * POW (1-1/N, N ).

 

Summary:

For this question, if we use the previous experience to calculate the probability strictly according to the standard, the problem may be more complicated or cannot be calculated at all. That is to say, we need to calculate the probability of an empty box being 1, and the probability of an empty box being 2 ...... In the end, it is impossible to calculate the order, but here we change the way of thinking, and the problem has been solved as quickly as possible.