Question 715533: Twenty-six tiles with each of the 26 letters of the alphabet printed on them are placed in a box. If three tiles are selected from the box, with replacement, what is the probability that the tiles selected will spell the word ADD? The letters must be selected in the correct order.
Answer by Positive_EV(69)   (Show Source):
You can put this solution on YOUR website! The probability of getting ADD in that order is the probability of selecting an A then a D, then the D again. There are 26 tiles in the bag, and for every draw there is one specific letter you need to make the word ADD. Because the tile is replaced, this makes the probability of getting that one letter you need during each draw 1/26. There are three draws, and you need to get the right letter for all of them. The probability is P(A first)*P(D second)*P(D third) = (1/26)*(1/26)*(1/26) = 1/17576.
Replacement is important here, as if this were done without replacement, that second D would be very difficult (read: impossible) to get.
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