Probability question

[Agent Smith]

A bag contains 4 red balls, 3 green balls, and 2 blue balls. You pick a random ball.

P(ball is red) = P(R) = 4/9
P(ball is green) = P(G) = 3/9
P(ball is blue) = P(B) = 2/9

P(ball is not red) = P(~R) = 3/9 + 2/9 = 5/9

What is the probable color of the random ball you picked?

1. P(~R) > P(R). So the ball is probably not red i.e. it's probably green or blue.

2. P(R) > P(G) and P(R) > P(B). So the ball is probably red than green and also it's probably red than blue.

Are the 2 conclusions above (1 and 2) in conflict? 1 is saying the ball's probably not red and 2 is saying it probably is red.

 

[BigBeachBanana]

What is the probable color of the random ball you picked?

What's most probable is you haven't thought about this. Your posts are purposely disingenuous.

Relative vs. Absolute Probabilty

An opaque bag contains 4 red balls, 3 green balls, 2 yellow balls and 1 white ball. Total number of balls = 10 You are to pick a ball at random from this bag. P(red ball) = P(R) = \frac{4}{10} = 40% P(green ball) = P(G) = \frac{3}{10} = 30% P(yellow ball) = P(Y) = \frac{2}{10} = 20% P(white...

mathforums.com

 

[Agent Smith]

What's most probable is you haven't thought about this. Your posts are purposely disingenuous.

Relative vs. Absolute Probabilty

An opaque bag contains 4 red balls, 3 green balls, 2 yellow balls and 1 white ball. Total number of balls = 10 You are to pick a ball at random from this bag. P(red ball) = P(R) = \frac{4}{10} = 40% P(green ball) = P(G) = \frac{3}{10} = 30% P(yellow ball) = P(Y) = \frac{2}{10} = 20% P(white...

mathforums.com

You're not the first one to say and probably not the last one too.

How is it disingenuous? There's little room for that, no?

My issue, as a clarificatory addendum:
Though there are (relatively) more red balls, it's unlikely that a random ball is red. I find this at least counterintuitive, if not a full-blown paradox. I'm unable to answer the question "is a random ball likely to be red?"

 

[Agent Smith]

To prove that I've actually been working on the problem:



These are the 2 probability distributions I could think of.
Figure A: The individual colored balls and their respective probabilities are given
Figure B: The green and blue probabilities have been clubbed together as non-red.

Which distribution answers the question: What color is a random ball likely to be?

 

[Steven G]

What is the probable color of the random ball you picked? NOT What is the probable color of the random ball you didn't picked?
You pick 1 color, NOT 2 colors

 

[Agent Smith]

What is the probable color of the random ball you picked? NOT What is the probable color of the random ball you didn't picked?
You pick 1 color, NOT 2 colors

It's probably not red, since we have there are more non-red balls (5). than red ones (4).

But it's likelier red than blue and likelier red than green because red balls (4) outnumber the green ones (3) AND the blue ones (2).