SOLUTION: Four letters and envelopes are addressed to four different people. If the letters are randomly inserted into the envelopes, what is the probability that(a) exactly one is inserted

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Question 75535This question is from textbook Precalculus with limits
: Four letters and envelopes are addressed to four different people. If the letters are randomly inserted into the envelopes, what is the probability that(a) exactly one is inserted and (b) at least one is inserted in the correct envelopeThis question is from textbook Precalculus with limits

Answer by stanbon(48568) About Me  (Show Source):
You can put this solution on YOUR website!
Four letters and envelopes are addressed to four different people. If the letters are randomly inserted into the envelopes, what is the probability that(a) exactly one is inserted in the correct envelope:
P(success)=1/4
P(one correct of four)= 4C1 (1/4)^1(3/4)^3 = 4(27/256)=0.421875
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(b) at least one is inserted in the correct envelope
P(at least one) = 1 - P(none correct)
= 1 - 4C0(1/4)^0(3/4)^4
= 1 - 1*1*81/256
= 1 - 0.316
= 0.6835
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Cheers,
stan H.