A section of an exam contains four questions with \"True\" or \"False\" answers.

Question

A section of an exam contains four questions with "True" or "False" answers. A completed exam paper is selected at random, and the four answers are recorded. List all possible outcomes in the sample space. Assuming the outcomes to be equally likely, find the probability that all the answers are the same. Assuming the outcomes to be equally likely, find the probability that exactly one of the four answers is "True." Assuming the outcomes to be equally likely, find the probability that at most one of the four answers is "True."

Explanation / Answer

1) Sample Space = {TTTT, FFFF, FTTT, TFTT, TTFT, TTTF, TFFF, FTFF, FFTF, FFFT,

FFTT, TTFF, FTTF,TFFT, FTFT, TFTF} - n = 16

2) P(All the answers are same ) = P(all the answers are true) + P(all the answer are false)

= 1/16 + 1/16 = 2/16 = 1/8

3)

The probability that exactly one of the four answer is true is 4/16 = 1/4 = 0.25

4) P(at most 1 of the four answer is TRUE) = P(X<=1)

= P(X=0) + P(X=1)

= P(All are False) + P(exactly one of the answer is True out 4)

= 1/16 + 4/16 = 5/16

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