Use the promlem below, there are 4 blue marbles 5 red marbles 1 green marbles 2 black marbles in a bag suppose you select one marble at random find each probability of

P( not green)

Ronelyn Lynlyn
2022-05-31
Answered

Use the promlem below, there are 4 blue marbles 5 red marbles 1 green marbles 2 black marbles in a bag suppose you select one marble at random find each probability of

P( not green)

You can still ask an expert for help

karton

Answered 2022-08-01
Author has **439** answers

As per the given question;

The favorable event is that the selected marble is not green, that is, the selected marble is either blue or red, or black.

So, the total number of occurrences of the favorable event = (total number of marbles in the bag) - (number of green marbles in the bag) = 12-1 = 11

And, the total number of trials = total number of marbles in the bag = 12

So, the probability that the selected marble is not green in color

= (Total number of occurrence of the favorable event) / (Total number of trials)

= (number of non-green marbles in the bag)/(total number of marbles in the bag)

= 11/12 = 0.917

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For example, I know that H(X) can be interpreted as the average encoding length. But what does $H(Y|X)$ intuitively mean?

And what is mutual information? I read things like "It is the reduction in the uncertainty of one random variable due to the knowledge of the other". This doesn't mean anything to me as it doesn't help me explain in words why $I(X;Y)=H(Y)-H(Y|X)$. Or explain the chain rule for mutual information.

I also encountered the Data processing inequality explained as something that can be used to show that no clever manipulation of the data can improve the inferences that can be made from the data. If $X\to Y\to Z$ then $I(X;Y)\ge I(X;Z)$. If I had to explain this result to someone in words and explain why it should be intuitively true I would have absolutely no idea what to say. Even explaining how "data processing" is related to a markov chains and mutual information would baffle me.

I can imagine explaining a result in algebraic topology to someone since there is usually an intuitive geometric picture that can be drawn. But with information theory if I had to explain a result to someone at comparable level to a picture I would not be able to.

When I do problems its just abstract symbolic manipulations and trial and error. I am looking for an explanation (not these blah gives information about blah explanations) of the various terms that will make the solutions to problems appear in a meaningful way.

Right now I feel like someone trying to do algebraic topology purely symbolically without thinking about geometric pictures.

Is there a book that will help my curse?

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