Mathematical permutation and combination probability problem! ! ! A, B and C of the red team play Go with A, B and C of the blue team. The probabilities of A-to-A, B-to-B, C-to-C, known A-to-A, B-to-B and C-to-C are 0.6, 0.5 and 0.5 respectively, assuming that the results of each game are independent of each other.

What are the odds that three members of the red team will win?

0.6x0.5x0.5 = 0. 15

Use? The total number of sets won on behalf of the members of the red team. Distribution table and mathematical expectation.

The total number of sets won by members of the red team =0. Expectation = 0.4x0.5x0.5 = 0. 1.

The total number of disks won by members of the red team = 1 expectation = 0.6x0.5x0.5+0.4x0.5x0.5+0.4x0.5x0.5 = 0.35.

The total number of disks won by members of the red team =2. Expectation = 0.6x0.5x0.5+0.6x0.5x0.5+0.4x0.5x0.5 = 0.25x1.6 = 0.4.

The total number of sets won by members of the red team =3. Expected value = 0. 15.

Mathematical expectation = 0.35+0.8+0.45 = 1.6