re: Solve this OT

The answer is 50/50, forget about the balls

After you’ve picked a good ball you’re dealing with only 2 possible boxes at this point. 1 box will give you a gold ball .. The other will give you a silver ball.

/thread

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It's either gold or silver. That's true. That's two possible outcomes.

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And if it were that simple, the answer would be 50%

Clearly this isn't true. Framing it this way is an oversimplification, it leaves out the key details as to why the correct answer is 67%.

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And if it were that simple, the answer would be 50%

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Nope. Maybe you don't understand it as well as you thought. You can have only 2 possible outcomes with one having a greater probability than the other.

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MorgusTheMagnificent

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I Clicked the thread and solved riddle without reading everyone else’s convoluted answers.

If you don’t get 50%, I’m sorry, but you’re wrong

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However, saying there are three possible outcomes is also correct,

it can't be. It may help someone understand the probabilities though

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, it most certainly can be.

The next ball you pick is either gold or silver. Do you agree?

The next ball you pick is either G1, G2, or S1. Do you agree?

The next person is either male or female. The next person is either John, James, or Jill.

Surely you understand that both of these are correct. Arguing otherwise is like saying the colors of the rainbow are either red or not red, but refusing to see that's an oversimplification of the problem.

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50%

Anyone saying otherwise is a fricking dumbass

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Wooooooooo pig sooooie!

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I Clicked the thread and solved riddle without reading everyone else’s convoluted answers.

If you don’t get 50%, I’m sorry, but you’re wrong

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More like MorgusTheMoronic

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As always, it's time to get all Monte Carlo up in this bitch. This is in Python, and the leading dots on some of the lines just represent spaces that won't format correctly here any other way I've found. import random # Three boxes in the 'box' list, each box is # a list of two balls. box = [['G','G'],['G','S'],['S','S']] def choose_ball (): # We'll choose a box at random (and remember it) # and choose a ball from it. . this_box = random.randrange (3) . return (this_box, random.choice (box [this_box])) def other_ball (box_idx): # If we bother to look at the 'other' ball, we know # we have already chosen a 'G', so we must be in # either box [0] or box [1] # in box [0], the other ball has to be 'G', # in box [1], the other ball has to be 'S' . if box_idx == 0: .. return 'G' . if box_idx == 1: .. return 'S' trials = 0 golds = 0 # Now we do the test a million times for i in range (1000000): # Pick a ball and remember which box we're in . my_box, my_ball = choose_ball () . if my_ball == 'S': # Silver ball first -- don't count anything # Just do the next one .. continue . else: # Gold ball first, so we count this one # and look at the other ball in the box. .. trials = trials + 1 .. if other_ball (my_box) == 'G': ... golds = golds + 1 print (float (golds) / float (trials))

So, for each test, we pick a ball 1 million times. If we pick a silver ball, we go on to the next pick. If we pick a gold ball, we look at the other ball in the box we picked from. At the end we look at ONLY the times we picked a gold ball first, and we see the fraction of times that the other ball was also gold. It's fairly fast on a modern PC, so I ran it 10 times (remember it was a million picks for each run and another pick if we picked gold first).
Results are:
0.665746226428
0.667399396348
0.667402563641
0.667849064158
0.666473975721
0.665929128366
0.666613307294
0.666898288197
0.667379593472
0.666684691288

It's pretty safe to say that simulation agrees with the assertion that your chances are 2/3 to pick a second gold ball GIVEN that you've picked a gold ball first.

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Smarter than a computer program are you?

Look, there are three possible outcomes if you've pulled a random and unknown gold ball. All equally likely and all distinct from one another.

The two possible remaining gold balls, although both gold, are distinct from one another and get equal weight in the calculation of probable outcome. THIS is why the odds are 2/3 gold.