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You have two jars, 50 red marbles and 50 blue marbles. You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. When picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar. You can arrange the marbles however you like, but each marble must be in a jar.
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You have two jars, 50 red marbles and 50 blue marbles. You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. When picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar. You can arrange the marbles however you like, but each marble must be in a jar.
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You have 10 identical bottles of identical marble. Each bottle contain hundred of marbles. Out of 10 bottles 09 have 1 gram of marbles but 01 bottle has marbles of weight of 1.1 gram. Given a measurement scale, how would you find the heavy bottle? You can use the scale only once.
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A prisoner fate will be determined by a game. there are two jars, one with 100 white marbles, and one with 100 black marbles. at this point, prisoner is allowed to redistribute the marbles however he wish e.g. swap a black marble with a white marble, etc. the only requirement is that after prisoner is done with the redistribution, every marble must be in one of the two jars. Afterwards, both jars will be shaken up, and prisoner will be blindfolded and presented with one of the jars at random. then he pick one marble out of the jar given to him. if the marble prisoner pull out is white, prisoner live; if black, prisoner die. how should prisoner redistribute the marbles to maximise the probability that he live; what is this maximum probability (roughly)?
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A jar contains one hundred marbles, each of which may be white or black. You pull out 100 marbles with replacement, and they are all white. What is the probability that all one hundred marbles are white?
(Note: “With replacement” means you take out a random marble, look at its colour, then put that marble back. Then repeat.)
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