Probability
In a game there are two urns with 10 balls of the same size in each urn. The above table indicates the quantities of balls of each color in each urn.
A move consists of:
1) The player chooses a color of a ball, which in his opinion, will be removed from the urn 2, in step 3.
2) He takes randomly a ball from urn 1 and puts in the urn 2, mixing it with those that are there.
3) After, he removes, also randomly, a ball from the urn 2.
4) If the color of the ball removed from the urn 2 is the same as the initial guess, he wins the game.
What color should be chosen by the player so that it has the highest probability of winning?
Use the following list:
1-Yellow
2-Red
3-Green
4-White
5-Blue
If your answer is yellow type 1.
Image Source: ENEM 2012
The answer is 2.
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Whichever colored ball you choose from Urn 1 and put it to Urn 2, the probability of removing a red ball from Urn 2 is always highest . , i.e 4/11 . So therefore the player has to choose red as it has the highest probability of winning.