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 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}

Answer 1

Answer:

C) {S, FS, FFS, FFF}

Step-by-step explanation:

The person entering the code needs a success to access the cell phone or the person stops trying when he has failed at all 3 attempts. The possible outcomes are;

(1) The person is successful at first attempt {S}

(2) The person failed at first attempt, successful at second attempt {FS}

(3) The person failed at first and second attempts, successful at third attempt {FFS}

(4) The person failed at the three attempts {FFF}

The sample space is {S, FS, FFS, FFF}