Question

A section of an exam contains 6 True-False questions

A completed exam paper is selected at random, and the 6 True/False answers are recorded

a)List all outcomes in the sample space

b)Assuming the outcomes to be equally likely, find the probability that all the answers are the same

c)Assuming the outcomes to be equally likely, find the probability that exactly one of the 6 answers is True

d) Assuming the outcomes to be equally likely, find the probability that at most one of the 6 answers is True

Show all the steps, formulas, and calculations.

Answer 1

Solution

a.)

All 36 outcomes

FFFFFF	FFFFFT	FFFFTF	FFFTFF	FFTFFF	FTFFFF
TFFFFF	FFFFTT	FFFTTF	FFTTFF	FTTFFF	TTFFFF
TFFFFT	FFFTTT	FFTTTF	FTTTFF	TTTFFF	TTFFFT
TFFFTT	FFTTTT	FTTTTF	TTTTFF	TTTFFT	TTFFTT
TFFTTT	FTTTTT	TFTTTT	TTFTTT	TTTFTT	TTTTFT
TTTTTF	TFFFFT	TFFFTT	FTFTFT	TFTFTF	TTTTTT

b.)All answer are same={FFFFFF, TTTTTT}

Probability(All answer are same)=2/36

=1/18

c.)one of the 6 answer is true={ FFFFFT, FFFFTF, FFFTFF, FFTFFF, FTFFFF, TFFFFF}

probability of one of the 6 answer is true=6/36

=1/6

d.)at most one of the 6 answers is True={FFFFFT, FFFFTF, FFFTFF, FFTFFF, FTFFFF, TFFFFF, FFFFFF}

Probability at most one of the 6 answers is True=7/36