(a)  Having 4 optional answers to each question, of which only one is correct,

     the probability to guess the answer correctly is  , if to guess randomly.

     Therefore, the probability to guess all 6 answers correctly is   =  = 0.000244.    ANSWER  




(b)  Since the probability to guess answer correctly is    to each question, 

     the probability to answer incorrectly  is    for each question. 

     Therefore, the probability to guess all 6 answers incorrectly is   = 0.177979.     ANSWER



(c)  Before answering the last question (c), I'd like to notice that the post INCORRECTLY uses the notion / (the conception) 

     of mutually exclusive events, showing that the author of the post doesn't know the terminology in the subject.


     The correct term to use here is  "complementary probability".


     After making this notice, I am ready to continue.


     The probability to answer at least one question correctly is the COMPLEMENT to the probability to answer all questions incorrectly,

     i.e. the complement to the probability found in (b).


     Thus the answer to (c)  is  1 -  = 1 - 0.177979 = 0.822021.    ANSWER