a) the first correct answer is that of question 4
b) at most four questions must be answers to get the first correct answerIf a student answers questions on a true-false test at random?
I'm assuming ';at random'; means the following is true: The probability of any answer being right or wrong is 1/2, and the probability of any answer being right or wrong is independent of whether any other answer is right or wrong.
a. For this to happen, answers 1, 2, and 3 all must be wrong, and 4 must be right. So the probability is 1/2 * 1/2 * 1/2 * 1/2 = 1/16.
b. For this to happen, one of the first four answers must be right. The only way this doesn't happen is if all four of the answers are wrong. You can figure that probability out and then subtract from 1.
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