SOLUTION: A box contains six letters, shown as follows. What is the probability of the outcome DAN in that order if three letters are drawn one-by-one a. with replacement? b. without repla

Question 386673: A box contains six letters, shown as follows. What is the probability of the outcome DAN in that order if three letters are drawn one-by-one
a. with replacement?
b. without replacement? R A N D O M
Answer by gwendolyn(128) (Show Source): You can put this solution on YOUR website!
a) In the case of replacement, we need to pick the D out of all 6 letters (P = 1/6), then we need to pick the A out of all 6 (P = 1/6), then we need to pick the N out of all 6 (P = 1/6). We multiply the probabilities together since they must all occur. So, the answer is (1/6)*(1/6)*(1/6) or 1/216.
b) In the case without replacement, we must first pick the D out of all 6 letters (P = 1/6), then we must pick the A out of the remaining five letters (P = 1/5), then we must pick the N out of the remaining 4 letters (P = 1/4). We multiply the probabilities together since they must all occur. So, the answer is (1/6)*(1/5)*(1/4) or 1/120.
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