Problem No.1 A section of an exam contains four questions with \"True\" or \"Fal

Question

Problem No.1 A section of an exam contains four questions with "True" or "False" answers. A completed exanm paper is selected at random, and the four answers are recorded 1) List all possible outcomes in the sample space. 2) Assuming the outcomes to be equally likely,find the probability that all the answers are the same. 3) Assuming the outcomes to be equally likely,find the probability that exactly one of the 4) Assuming the outcomes to be equally likely, find the probability that at most one of the Solution four answers is "True." four answers is "True."

Explanation / Answer

here let true is represented by T and false by F.

1) sample space for all answers. {TTTT,TTTF,TTFT,TFTT,TTFF,TFFT,TFTF,TFFF,FFFF,FFFT,FFTF,FTFF,FFTT,FTTF,FTFT,FTTT}

total 16 outcmes

2) there are 2 outcomes with all answers same {TTTT,FFFF}

hence probability =2/16 =0.125

3) there are 4 outcomes with exactly one of four answers are true {,FFFT,FFTF,FTFF,,TFFF}

hence probability =4/16 =0.25

4)

there are 5 events with at most one of the answers is true {FFFT,FFTF,FTFF,,TFFF,FFFF}

hence probability =5/16=0.3125

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