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A person trying to gain access to a bank vault must pass through a series of three security doors. If an attempt to pass through a door is a failure, then the person will not make any further attempts. Let P denote a successful pass and F denote a failed pass. What is the sample space for this random experiment? S = {F, PF, PPF, PPP} S = {F, FP, FFP, FFF} S= {F, PF, PPF} S ={PPP, FPP, PFP, PPF, FFP, FPF, PFF, FFF} S = {P, PP, PPP}

Question

A person trying to gain access to a bank vault must pass through a series of three security doors. If an attempt to pass through a door is a failure, then the person will not make any further attempts. Let P denote a successful pass and F denote a failed pass. What is the sample space for this random experiment? S = {F, PF, PPF, PPP} S = {F, FP, FFP, FFF} S= {F, PF, PPF} S ={PPP, FPP, PFP, PPF, FFP, FPF, PFF, FFF} S = {P, PP, PPP}

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Solution

The sample space for this random experiment is S ={PPP, FPP, PFP, PPF, FFP, FPF, PFF, FFF}. This is because each door represents a trial with two possible outcomes (P or F), and there are three doors. Therefore, there are 2^3 = 8 possible outcomes.

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