<s>[INST] Here is a problem I need help with:
4. A surprising result of eight experiments is reported as follows:
Experiment 1: "Success" with probability 1/2, "Failure" with probability 1/2.
Experiment 2: "Success" with probability 7/8, "Failure" with probability 1/8.
Experiment 3: "Success" with probability 1/3, "Failure" with probability 2/3.
Experiment 4: "Success" with probability 1/8, "Failure" with probability 7/8.
Experiment 5: "Success" with probability 5/6, "Failure" with probability 1/6.
Experiment 6: "Success" with probability 2/5, "Failure" with probability 3/5.
Experiment 7: "Success" with probability 11/12, "Failure" with probability 1/12.
Experiment 8: "Success" with probability 1/11, "Failure" with probability 10/11.
Now a "success" occurs in every single one.
Is it more likely that, in fact, the reported probability numbers were actually all reversed, assuming (on that hypothesis) that all experiments are independent of each other?[/INST]