The answer depends on how well you do in the quiz: that is not a random experiment.
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If it is a T/F test; probability correct for each question is 0.5. Since there are 4 questions, raise 0.5 to the 4th power; e.g. (0.5)4. So, probability all correct is 0.0625. If a 4 part multiple choice, P(correct) = .25 so raise .25 to the 4th power, or .003906.
The conditional probability is 1/4.
Assuming it is a fair coin, the probability is 1/24 = 1/16.
The probability is 1/4
Probability of each question correct is 1/4 or 0.25. Since there are 5 questions, raise 0.25 to the 5th power or (0.25)5. So, probability all correct is 0.0009765.