16. A section of an exam contains four True-False questions. A completed exam paper is selected at random, and the four 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 four answers is "True." d. Assuming the outcomes to be equally likely, find the probability that at most one of the four answers is "True."

a

[ FFFF] , [FFFT] , [FFTF] , [FFTT]

[FTFF] , [FTFT] , [FTTF], [FTTT]

[TFFF] , [TFFT] , [TFTF] , [TFTT]

[TTFF] , [TTFT],[TTTF] , [TTTT]

b

c

d

Step-by-step explanation:

From the question we are told that

The number of True - False question is n = 4

The number of answers recorded are k = 4

Generally the outcomes in the sample space are 16 and they are listed below

[ FFFF] , [FFFT] , [FFTF] , [FFTT]

[FTFF] , [FTFT] , [FTTF], [FTTT]

[TFFF] , [TFFT] , [TFTF] , [TFTT]

[TTFF] , [TTFT],[TTTF] , [TTTT]

Generally from the list of the possible outcome we see that the number of outcome where the answers are the same is 2 i.e [TTTT] and [FFFF]

So the probability that all the answers are the same is mathematically represented as

=>

Generally from the list of the possible outcome we see that the number of outcome where exactly one answer is true is 4 i.e [FFTF] , [FFFT],[TFFF] , [FTFF]

So the probability that exactly one of the four answers is "True." is mathematically represented as

=>

Generally from the list of the possible outcome we see that the number of outcome where at most one of the four answers is true is 5 i.e [FTFF] , [FFFF] , [FFTF] , [FFFT] ,[TFFF]

So the probability that at most one of the four answers is mathematically represented as

6 (3) - 4 + 32

hope this