Drone Probabilites

[TheReMiXeR]

The drone landing is carried out by two commands: up and down, which are transmitted with probabilities of 0.25 and 0.75, respectively.

The probability of command distortion under the influence of interference, namely, the transformation of the “up” command into the “down” command is 0.1, and the “down” command into the “up” command is 0.2. The drone received the command "down". What is the probability that it was transmitted:
a) a distorted "up" command.
b) really command "down"
I got the wrong answers, now I don’t fully understand what the problem is, please help!
Sorry that the solution is in Ukrainian, but I think it's clear how I did it. I can't figure out what's wrong

 

[Dr.Peterson]

The drone landing is carried out by two commands: up and down, which are transmitted with probabilities of 0.25 and 0.75, respectively.

The probability of command distortion under the influence of interference, namely, the transformation of the “up” command into the “down” command is 0.1, and the “down” command into the “up” command is 0.2. The drone received the command "down". What is the probability that it was transmitted:
a) a distorted "up" command.
b) really command "down"
I got the wrong answers, now I don’t fully understand what the problem is, please help!
Sorry that the solution is in Ukrainian, but I think it's clear how I did it. I can't figure out what's wrong

We'll be able to understand what you wrote better if you at least define your notation. What do A₁, B₁, P_A1(B₁), P(B₁)A₁,and so on mean?

 

[Dr.Peterson]

We'll be able to understand what you wrote better if you at least define your notation. What do A₁, B₁, P_A1(B₁), P(B₁)A₁,and so on mean?

I very much hoped you would respond, so we could talk about this a little more. You are probably close to a correct answer, but it is too hard to compare your work to mine without knowing your meaning.

My guess is that A₁ means something like "drone receives down command", B₁ means something like "down command was sent", and A₂ and B₂ are their negations. (I may have that all twisted.)

I suspect your notation P_A(B) is equivalent to what I would write as P(B|A), meaning the conditional probability of B given A. I don't know what you mean by the notation P(A)B, unless you meant to write the same thing.