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A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful, however he cannot try more than 3 times or the phone will lock him out. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experime

Question

A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful, however he cannot try more than 3 times or the phone will lock him out. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experime

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Solution

The sample space for this random experiment includes all possible outcomes of the person's attempts to unlock his phone. Each attempt can either be a success (S) or a failure (F), and he can make up to 3 attempts. Therefore, the sample space is as follows:

  1. S (he succeeds on the first try)
  2. FS (he fails on the first try, but succeeds on the second)
  3. FFS (he fails on the first two tries, but succeeds on the third)
  4. FFF (he fails on all three tries and is locked out)

So, the sample space is {S, FS, FFS, FFF}.

This problem has been solved

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