Question 480257
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If you were to reach in the bag, pull out 1 ball, check to see if it is red or not, THEN REPLACE IT and repeat the experiment twice more, then your method would produce the correct probability, namely 1 minus the binomial distribution of zero successes in 3 trials where the success of one trial is 1/3.  Notice that you have to do it with replacement because if you don't, the probability of a red changes on each trial (either by reducing the denominator of the single trial probability fraction by one if you DON'T get a red, or reducing both the numerator AND denominator by one if you DO get a red).  Note that the binomial distribution works for the dice game because you are always replacing -- that is you never remove any spots from your dice before rolling them another time.


However, the experiment described is performed by reaching in the bag, grabbing 3 marbles and checking to see if any of them are red.  Different experiment -- different results.  Here you need the number of ways the single outcome could be zero reds, namely 12 choose 3, divided by the number of ways to draw 3 balls at once, namely 18 choose 3 and then subtract that result from 1.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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