roblem No. 1. 0pe Given A section of an exam contains 5 True-False questions. A

Question

roblem No. 1. 0pe Given A section of an exam contains 5 True-False questions. A completed exam paper is selected at random, and the 5 True/False answers are recorded. (1) List all 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 5 answers is True. (4) Assuming the outcomes to be equally likely, find the probability that at most one of the 5 answers is True. Solution

Explanation / Answer

We solve this problem using the basic principles:

5 TF problems. Hence,

1. All outcomes

TTTTT
TTTTF
TTTFF
TTFFF
TFFFF
FFFFF
FFFFT
FFFTT
FFTTT
FTTTT
FTFTF
TFTFT
TFFTF
FTTFT
TFFFT
FTTTF
FTFFF
FFTFF
FFFTF
TFTTT
TTFTT
TTTFT
FFTTF
TTFFT
FTFFT

2. All answers are the same: i.e. All T or All F = {TTTTT,FFFFF}

So, P( all answers are the same ) = 2/25 = .08

3. P(Exactly 1 of them is True) = 5C1 / 25C1 = 5/25 = 1/5 = .20

4. P(Atmost 1 of them is True) = 5+1 /25 = .24

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