Here is the problem:
A student is worried that the metro system might not operate properly when he goes home on a given day. There are two reasons for his worries: it is really
Coldoutside, and they may be working on the construction of metro
Extension. He estimates that the risk of failure due to the cold weather is
20%. Independently, they may shut down traffic due to the metro Extension plans with a probability of
How unpredictable is it that the student may not be able to take the subway home, i.e. that the trains are cancelled, either because of the cold weather or due to the construction work (or both)? Answer in terms of entropy, measured in bits.
$$ P(W \lor C) = 1 − P(\neg W)P(\neg C) = 1 − 0.40 = 0.60 \\ ent = −0.6 \log_2(0.6) − 0.4 \log_2(0.4) \approx 0.971 $$
I can understand lets say that 0.6 where it came from and why, but that 0.4 I cannot really what it represents for the student at all.
My approach (which is wrong apparently) is: $ ent = −0.2 \log_2(0.2) − 0.5 \log_2(0.5) −0.1 \log_2(0.1) ≈ 1.28 $, where 0.1 is $0.5 \times 0.2 $ since events are independent.` To my understanding, my expression reads: probability it's cold, or probability there are contractions, or both. What does the correct answer expression read in layman terms?