Predicting Rainfall in a Village: Understanding the Necessary Information

[svm]

In some village rain falls with probability of 0.5 (statistically), e.g. tomorrow it may or may not fall, the chances are equal.

A local meteorologist gathers information, allowing him only to predict rain falling in the village with average success rate of 75% (about 3 of 4 predictions are correct).

What amount of information allows him to predict rain falling for a given day?
(The information is meaningful only for this particular prediction, no other uses are possible)

 

[CRGreathouse]

You only need 1 bit to learn it perfectly (-lg 0.5), so you're talking about fractions of a bit. I get about 0.42 bits.

 

[svm]

You only need 1 bit to learn it perfectly (-lg 0.5), so you're talking about fractions of a bit. I get about 0.42 bits.

Hm... That's interesting. My answer was only about 0.19 bit:
1 - (- 0.75 * lg 0.75 - 0.25 * lg 0.25) bit

Am I wrong?

 

[CRGreathouse]

Hm... That's interesting. My answer was only about 0.19 bit:
1 - (- 0.75 * lg 0.75 - 0.25 * lg 0.25) bit

Am I wrong?

You're right, I wasn't answering your question. I was saying how much information there was in the 75% prediction total. (Sorry!)