Solution

 

b. The total number of possible outcomes of 6 tosses is $2^6$, by $mn$ rule. Each outcome is equally likely. Thus, $P(\textrm{ all six tosses result in tails)})= \dfrac{1}{2^6}.$

c. Each choice is not equally likely as was the case in coin tossing. The student who has studied is more likely to give right answer and the probability of matching when students have studied would be higher than $\dfrac{1}{8}.$

$Answer$

a. $\dfrac{1}{8}$ b. $\dfrac{1}{2^6}$ c. No

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