p(X = 0)= 1 *(2 * 1/6 * 5)= 1/ 15

P

(X = 1)= 2 *(4 * 2 * 1/6 * 5 * 4)= 2/ 15

p(X = 2)= 3 *(4 * 3 * 2 * 1/6 * 5 * 4 * 3)= 3/ 15

p(X = 3)= 4 *(4 * 3 * 2 * 2 * 1/6 * 5 * 4 * 3 * 2)= 4/ 15

p(X = 4)= 5 *(4 * 3 * 2 * 2 * 1 * 1/6 * 5 * 4 * 3 * 2 * 1)= 5/ 15

The mathematical expectation is: 0 * (115)+1* (2/15)+2 * (3/15)+3 * (4/15).

Rule: As long as you can figure out the first and second methods and the number of genuine products to be inspected, the number of pieces to be inspected can be made at one time. After determining the number of inspected genuine products, the sequence of them and two mixed defective products is equal to the corresponding value of X plus 1, and the corresponding probability is obtained by multiplication.

(For reference only)