A box contains 6 letters, shown as CRATED. What is the probability of the outcome CARE in that order if 4 letters are drawn one by one (a) with replacement? (b) without replacement?
a) In the case of replacement, we need to pick the C 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 R out of all 6 (P = 1/6), then
we need to pick the E 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)*(1/6) or 1/1296.
b) In the case without replacement, we must first pick the C 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 R out of
the remaining 4 letters (P = 1/4), , then we must pick the E out of
the remaining E letters (P = 1/3). We multiply the probabilities
together since they must all occur. So, the answer is
(1/6)*(1/5)*(1/4)*(1/3) or 1/360.
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