The tangent slope is 3a^2, and the tangent is y = 3a 2x-2a 3.

The intersection with the X axis and the Y axis is (2a/3,0) (0,-2a/3).

Area: 2/3 = 1/2 2a/3 2a 3

D: a= plus or minus 1

Will the sample be put back or not?

Well, if you don't put it back, when you draw an A for the third time, there will be only n-2 people left. The probability of winning the prize for the third time is 1/(n-2), and the probability of not winning the prize is

(n-3)/(n-2), and their ratio is 1:3.

So 1:(n-3)= 1:3.

n=6

The probability of the third lottery is 1/4.