SOLUTION: . Someone has arrived at a hotel and his suitcase is locked with a three-digit combination lock. Each digit of this lock has been set to digits from 0 to 9. Unfortunately, he forg

Click here to see ALL problems on Probability-and-statistics

Question 1202079: . Someone has arrived at a hotel and his suitcase is locked with a three-digit combination
lock. Each digit of this lock has been set to digits from 0 to 9. Unfortunately, he forgot the
right combination for the lock.
What is the probability that the suitcase can be opened on the first attempt when he …
a) no longer remembers any of the digits of the combination? _______
b) remembers that there is exactly one “7” among these digits? _______
c) remembers that the “7” is the first digit and that there is exactly one “7”?
Answer by ikleyn(52803) (Show Source):
You can put this solution on YOUR website!
Someone has arrived at a hotel and his suitcase is locked with a three-digit combination
lock. Each digit of this lock has been set to digits from 0 to 9. Unfortunately, he forgot the
right combination for the lock.
What is the probability that the suitcase can be opened on the first attempt when he …
a) no longer remembers any of the digits of the combination? _______
b) remembers that there is exactly one “7” among these digits? _______
c) remembers that the “7” is the first digit and that there is exactly one “7”?
~~~~~~~~~~~~~~~~

(a) There are 10*10*10 = 1000 possible combinations, and exactly one of them works. The probability to guess at first trial is . (b) Then he needs to try only these combinations 7xy, x7y, xy7 - in all 3*10*10 = 300 combinations. Exactly one of them works. The probability to guess at first trial is . (c) Then he needs to try all 9*9 = 81 combinations 7xy, where x and y are the digits from 0 to 9, except of 7. Exactly one of them works. The probability to guess at first trial is .

Solved.