[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 517
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Huh, well, if they take turns pulling balls out of the same bag, then the reasoning would be different - Petya took out the red one, and Vasya can't take it out anymore. Vasya's probability is zero :) If they each have a bag with one and the same set of marbles, the probability is calculated elementary here as well.
In general, judging by the picture, the problem is similar to the ones they write in the corridor on the blackboards at foreign universities. Those who have seen the film "Good Will Hunting" will understand the boards I am talking about.
It's a pity the condition of the problem is not formulated accurately. You have to figure it out for yourself.
No, no, Petya returns the stretched-out one and remembers the colour.
Alexei, where does it say that Petya needs something out of the bag?
I don't see where you're going with this, namesake...
No, no, Petya returns the drawn one and remembers the colour.
At this rate, you could say that everyone is pulling a ball out of their bag. So it's a tuple of two discs of 4 elements each. The number of possible combinations would be = 4 to the power of 2 = 16.
The winning ones are 1-1, 1-1', 1'-1, 2-2, 3-3. Probability will be = 5/16 = 0.3125. Approximately one third :)
You guys are a real piece of work, aren't you?
1. Nowhere in the conditions of the problem was it mentioned that Petya is limited to a list of colours of balls from the bag
2. There is no relationship between Petya and Vasya, so conditional probabilities are irrelevant.
Why argue, it's 50/50. Either you guessed it or you didn't :)