SOLUTION: Your debit card pin number contains 5 digits: 2 sixes, 2 threes and ends in a 5. What is the probability that you fail to guess the pin correctly (in other words you get it wrong t

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: Your debit card pin number contains 5 digits: 2 sixes, 2 threes and ends in a 5. What is the probability that you fail to guess the pin correctly (in other words you get it wrong t      Log On

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Question 625236: Your debit card pin number contains 5 digits: 2 sixes, 2 threes and ends in a 5. What is the probability that you fail to guess the pin correctly (in other words you get it wrong three times).
Answer by Edwin McCravy(8908) About Me  (Show Source):
You can put this solution on YOUR website!
There are 6 possibilities

{33665, 36365, 36635, 63365, 63635, 66335}

We will assume you will not try the same number twice.

We use the principle that "AND corresponds to MULTIPLICATION":

The probability of

%28matrix%286%2C1%2C%0D%0A%0D%0Agetting%2Cit%2Cwrong%2Cthe%2Cfirst%2Ctime%29%29matrix%286%2C1%2C%0D%0A%0D%0A%27%27%2C%27%27%2Cand%2C%27%27%2C%27%27%2C%27%27%29%28matrix%286%2C1%2C%0D%0A%0D%0Agetting%2Cit%2Cwrong%2Cthe%2Csecond%2Ctime%29%29matrix%286%2C1%2C%0D%0A%0D%0A%27%27%2C%27%27%2Cand%2C%27%27%2C%27%27%2C%27%27%29%28matrix%286%2C1%2C%0D%0A%0D%0Agetting%2Cit%2Cwrong%2Cthe%2Cthird%2Ctime%29%29 = P%28matrix%286%2C1%2C%0D%0A%0D%0Agetting%2Cit%2Cwrong%2Cthe%2Cfirst%2Ctime%29%29×P%28matrix%286%2C1%2C%0D%0A%0D%0Agetting%2Cit%2Cwrong%2Cthe%2Csecond%2Ctime%29%29×P%28matrix%286%2C1%2C%0D%0A%0D%0Agetting%2Cit%2Cwrong%2Cthe%2Cthird%2Ctime%29%29 = 5%2F6×4%2F5×3%2F4 = 1%2F2

Edwin