HW02_2011 solution

# HW02_2011 solution - Problem Set 2 Solutions(1 Number of...

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Problem Set 2 Solutions (1) Number of total possible outcomes is 4! = 24 . Number of selections of 2 correctly placed envelops is C 2 4 = 6 . In the 2 correctly placed envelops, there is only one possible way to assign letters, i.e. the correct way. And in the two miss placed envelops, there is also only one way to assign letters, i.e. the swapped way. So the number of outcomes with exactly two letters will go to the correct envelop is 6 ° 1 ° 1 = 6 . The probability is 6 = 24 = 0 : 25 . The probability of exactly three letters go into correct envelops is 0 . Because if three letters go to into the correct envelop, the rest of letter and envelop will automatically match correctly. So the number of correct match will be four. It is impossible to have exact 3 letters go into correct envelop. (2) Assuming that the °rst passenger get o/ at one of the seven ±oors, the second passenger must get o/ at one of the remaining six ±oors in which the passenger 1 does not get o/ and the probability of this case is 6/7.

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