Probability of putting back the lottery ticket

A: The probability of winning the red ball for the first time is 1/3, and the probability of winning the red ball for the second and third time is 1/3. So P (a) = (1/3) 3 = 1/27.

B: The probability that the first draw is not a black ball is 2/3, and the second and third draws are also 2/3, so P (b) = (2/3) 3 = 8/27.

C: Completely different means that the colors of the three balls are all different, that is, the arrangement of red, yellow and black, that is, there are three balls! Species =3*2=6, there are 3*3*3=27 possibilities in total, so the probability that the three colors are completely different is 6/27=2/9.

There is another way of thinking: no matter what color you choose for the first time, the color you choose for the second time is different from the color you choose for the first time, that is, 2/3.

The third time, you can only choose a fixed color. The probability is 1/3.

So P(C)=(2/3)*( 1/3)=2/9.

D: As can be seen from the question in A, the probability of being a red ball for three times is 1/27, so the probability of being a yellow ball or a black ball for three times is also 1/3.

The total * * * is 3/27= 1/9. Incomplete means not exactly the same. So P(C)= 1- 1/9=8/9.