.
It is a nice problem; therefore, I edited your post to make your formulation more clear.
A shipwreck threw you up away to inhabitant island.
You send out three messages for help:
- a smoke signal that has the probability of 0.1 of being seen;
- a message in a bottle that has the probability of 0.2 of being found, and
- a carrier pigeon that has the probability of 0.3 of arriving.
Find the probability your message will reach people and you will be saved, assuming
that these three signaling methods, smoke, bottles, and pigeons are independent.
Solution
Let's consider the complement event, that your message will not reach a resque crew.
The probability of this event is the product
P = (1-0.1)*(1-0.2)*(1-0.3) = 0.9*0.8*0.7 = 0.504.
Therefore, the probability that your message will reach people is the complement to it, i.e.
P' = 1 - 0.504 = 0.496. ANSWER
Solved.