Then I think you may not understand the meaning of pi. Look carefully, it is "the cumulative score of a drug is me …" rather than "the final score of a drug is me". There is a difference between the two. The cumulative score is not necessarily the final score, but the final score must be the cumulative score.

The following may be a little inconsistent with your question. If you have time, take your time or skip to the penultimate paragraph, but it may be a bit confusing. )

What do you mean by cumulative score? It is the score we got at this time of the experiment, which can also be understood as the current score of the experiment. For example, our initial score is 4, right, and then we assume that-1 has done two experiments, so now our cumulative score is 2, and p2 represents the probability that we think a drug is more effective after completing the experiment (there is something wrong with the expression here, and p2 will not change with our experimental situation).

When the cumulative score is 0, there will be 4 more mice cured by drug B than drug A, and the experiment will stop, so drug B is more effective, so p0=0, p8 is the same. In fact, the final score is only 0 or 8.

Then, if we get the value of p4, we can predict the probability of experiment failure without doing experiments (because the cure rate of drug A in the topic is low, it is a wrong conclusion to think that drug A is more effective), which is the purpose of the last question of this topic.

So p 1 is not equal to 0, because even if the score of drug A is 1 now, it may be considered more effective (for example, the score of drug A in the next seven experiments is+1), but this probability is extremely low.

However, if the current score is I, then the probabilities of the three results of the next experiment:-1, 0, 1 correspond to A, B and C in the topic respectively. If you get-1, then the next cumulative score is pi- 1, and the probability of pi will naturally be affected by pi- 1, so pi should be added with a pi- 1 (the probability of the next i- 1 × if the cumulative score is i- 1 Adding b pi and c pi+ 1 is the origin of pi = a pi-1+b pi+c pi+1in the title.

Therefore, in fact, "p0=0, p8= 1, PI = A PI-1+B PI+C PI+1"in the title can be obtained without giving, but if you do this, the teacher may be killed.