Maybe someone took a course from TSU on the styopik and knows the answer, any help would be appreciated. A very long entry:
Earthlings remotely probing planetary system of star galaxy Prob Measure for the content of hydrogen in the atmosphere. Sends one signal on each planet. The signal on the return path passes through the relay station, located on the border of the Solar system, and with probability 0.1 does not reach the Earth. All the results are stored at this station. If the result of the sensing, come to Earth, suggests that the percentage of hydrogen above a certain threshold (a positive result), then to this planet from Earth is sent immediately and automatically probe for a more detailed study (probe, in particular, it determines the content of hydrogen in the planet's atmosphere and transmits a corresponding signal to the Ground without interference). In case of negative result, the probe is sent.
In the event of a signal loss when passing through the intermediate station of the machine makes the decision about sending of the probe, tossing a fair die: if you roll a 6, then the probe is sent, otherwise not sent.
Method for remote studies are not accurate: if the result of sensing positive, then in fact the percentage of hydrogen above a given threshold with a probability of 0.8; if the sensing result is negative, then in fact the percentage of hydrogen does not exceed a given threshold with a probability of 0.95.
On the basis of the data stored at a relay station in the study of similar planetary systems of the galaxy Measure, for every planet of its star system Prob the result of remote sensing is expected to positive with a probability of 0.3.
Now, the question.
The result of remote sensing of planet Y system stars Prob on the Ground never came. Y was sent to the probe, which gave us accurate information about what percentage of hydrogen content in the atmosphere Y enough. What is the probability that the result of its remote sensing stored at an intermediate station, was positive?
A probability tree from the author of the course:
Don't get me wrong, but your arguments are not even going to try to list because I tried 50 different solutions, none came up in my head.
Thanks in advance!