SOLUTION: Suppose you have a key ring with eight keys on it, one of which is your house key. Further suppose you get home after dark and cant see the keys on the key ring. You randomly try o
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-> SOLUTION: Suppose you have a key ring with eight keys on it, one of which is your house key. Further suppose you get home after dark and cant see the keys on the key ring. You randomly try o
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Question 957876: Suppose you have a key ring with eight keys on it, one of which is your house key. Further suppose you get home after dark and cant see the keys on the key ring. You randomly try one key at a time, being careful not to mix the keys you have already tried with the ones you have not. What is the probability that you get the right key on the fifth try. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the probability of getting the key right on any one try is 1/8.
the probability of getting the key wrong on any one try is 7/8.
in order to get the key on the fifth try, you have to have failed on tries 1 to 4.
once you get the key you can stop.
the probability of failing on the first 4 tries and getting it on the fifth try is equal to 7/8 * 6/7 * 5/6 * 4/5 * 1/4.
the probability is therefore (7 * 6 * 5 * 4 * 1) / (8 * 7 * 6 * 5 * 4) which is equal to 1/8.
the probability is the same whether you are looking for the probability of getting it on the first try or on the second try or on the third try, etc.
