There are 10 inspection lots in the box, three of which are difficult to sign, and now two have been taken away. What is the probability that any of the remaining lots will not be difficult to sign?

Probability theory and mathematical statistics.

10 signature, 3 difficult to sign, 2 signatures have been taken away.

There are three kinds of signatures: 1, and both signatures are difficult to sign. One of the two signatures is difficult to sign. It is not difficult to sign both of them.

The first case:

The probability of the selected two difficult signatures =C3.2 (subscript 3, superscript 2, and so on) //C 10.2.

The probability that the remaining eight are not difficult to sign is 7/8.

Therefore, the probability of drawing is not difficult to sign =C3.2/C 10.2 × 7/8.

The second case:

The two drawn lots are 1 difficult to sign = c 3.1* c 7.1/c10.2.

The probability that the remaining eight are not difficult to sign is 6/8.

Therefore, the probability of drawing is not difficult to sign = c 3.1* c 7.1/c10.2× 6/8.

The third situation:

The probability of whether the two draws are difficult to sign = c7.2/c 10.2.

The probability that the remaining eight are not difficult to sign is 5/8.

Therefore, the probability of drawing is not difficult to sign =C7.2/C 10.2 × 5/8.

The sum of the results of three situations is the answer you want:

c 3.2/c 10.2×7/8+c 3. 1 * c 7. 1/c 10.2×6/8+c 7.2/c 10.2×5/8

I made it myself, it should be right ~ ~ ~