Help: A psychology professor gives a surprise quiz consisting of 4 true/false?

A psychology professor gives a surprise quiz consisting of 4 true/false


questions, and he states that passing requires at least 3 correct responses. Assume that an unprepared student adopts the questionable strategy of guessing for each answer.





a. Find the probability that the first responses is incorrect and the other


three are correct.





b. Is there any other arrangement of 3 correct and 1 incorrect responses whereby the student will pass the quiz? If so, give an example and calculate its probability of occurrence.Help: A psychology professor gives a surprise quiz consisting of 4 true/false?
a. .5 * .5 * .5 * .5 = .0625





b. C = correct, W = wrong





Here are the possible arrangments:





WCCC


CWCC


CCWC


CCCW





Each one has a probability of .0625, therefore the student has a 4*.0625 = .25 = 25% chance of passing the quiz.