algebra story problem

Question

You have a surprise true false quiz in english class . There are six questions if you guess at all of them what is the probability that you get all six.

Answer 1

2⁶=64 possible combinations of true-false answers

the probability is 1/64

suppose you had 3 questions (R=right and W=wrong)

RRR

RRW

WRR

RWR

WWW

WWR

RWW

WRW

the probability of getting all 3 right is 1/8 (2³=8 and only 1 is RRR)

Answer 2

It may help to forget about T-F for a moment;  just consider R-W (right-wrong).  If the probability of getting each of the questions right or wrong (that is, a guess and also random T-F answer key), then the events are independent and the probability of getting all 6 questions right is:

   P = (1/2)*(1/2)*(1/2)*(1/2)*(1/2)*(1/2) = 1/64