How to find the conditional probability in this problem from the TSU online course?

Question

Mathematics

Maybe someone took a course from TSU on the steppe and knows the answer, I will be glad for any help. Very long intro:

Earthlings are remotely probing the planetary system of the Prob star of the Measure galaxy for hydrogen content in the atmosphere. One signal is sent to each planet. The signal on the way back passes through a relay station located on the edge of the solar system, and with a probability of 0.1 does not reach the Earth. All results obtained are stored at this station. If the sounding result that came to Earth indicates that the percentage of hydrogen is above a certain threshold (positive result), then a probe is automatically sent from Earth to this planet for a more detailed study (the probe, in particular, accurately determines the hydrogen content in the atmosphere planets and transmits the corresponding signal to Earth without interference). If the result is negative, the probe is not sent.
If the signal is lost during transmission through the intermediate station, the automaton decides to send a probe by throwing the correct die: if 6 rolls, then the probe is sent, otherwise it is not sent.
The remote sensing method is not accurate: if the sounding result is positive, then in fact the percentage of hydrogen exceeds the specified threshold with a probability of 0.8; if the sounding result is negative, then in fact the percentage of hydrogen does not exceed the specified threshold with a probability of 0.95.
Based on the data stored at the relay station during the study of similar planetary systems in the Measure galaxy, for any planet in the Prob star system, the result of remote sensing is expected to be positive with a probability of 0.3.

Now the question itself.

The result of remote sensing of planet Y of the Prob star system did not reach Earth. A probe was sent to Y, which gave us accurate information that the percentage of hydrogen in the atmosphere of Y is sufficient. What is the probability that her remote sensing result, stored at the way station, was positive?

There is such a probability tree from the author of the course:

Do not misunderstand, but I will not even try to give my reasoning, because I have already tried 50 different solutions, none of them fit and my head is a complete mess.
Thanks in advance!

Answer 1

UPDATED:
Total probability that the ship will come and find H 0.275
The probability of the hypothesis that the remote probe will find H 0.3 The
conditional probability that H will be found with a positive forecast is 0.8
0.3*0.8/0.275 = 0.8727
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See
Scan the system 1000 times
Signal reached 1000*0.9 times, left branch
What is the total probability what is hydrogen?
900*0.3 times it seems to be positive, 900*0.3*0.8 times is actually positive
900*0.7 times we don't send probe and 900*0.7*0.05 times there actually positive level
(900*0.3*0.8 + 900*0.7*0.05)/900 = 0.275
Now there is no signal and we don’t care whether the probe will fly or not, the probability is the same