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.
1. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experiment?
a. {SSS, SSF, SFS, FSS, SFF, FSF, FFS, FFF}b. {S, FS, FFS}c. {S, FS, FFS, FFF}d. {S, SS, SSS}e. {S, SF, SSF, SSS}

For this case, we know that a person is trying to enter a 4 digit code to gain access to his cell phone, and we know that the person cannot try more than 3 times or the phone will lock him out.

We denote the following events S= Successful attempt , F= Failed attempt

And we are interested in the sample space, we must remember that the sample is the set with all possible values for an experiment.

For this case, the person could succeed in 1.2, 3 attempts or fail in the 3 attempts

For the case that is successful in the 1 attempt, we have S

For the case that is successful in the 2 attempt implies that the first attempt failed and we have FS

For the case that is successful in the 3 attempt implies that it fails in the first and second attempt and we have FFS

And the last option is that the person fails in all 3 trials and we have FFF

Then the sample space would be given by:

C. {S, FS, FFS, FFF}