Astudent randomly guesses the answers to a five question true/false test. if there is a 50% chance of guessing correctly on each question, what is the probability that the student misses exactly 1 question?

The probability that the student misses exactly 1 question is 15.625%

Step-by-step explanation:

From the question, there is a 50% (0.5) chance of guessing correctly. As such, there is also a 50% (0.5) chance of guessing wrongly where;

Let the chance of guessing the answer to a question correctly be T

And the chance of guessing the answer to a question wrongly be F

If the student misses exactly one question out of five, the possible scenarios or outcomes for this exercise are

F or TFTTT or TTFTT or TTTFT or F

Therefore, the probability that the student misses exactly 1 question (knowing that "or" in probability is equivalent to + while "and" is equivalent to ×)

= (0.5 × 0.5 × 0.5 × 0.5 × 0.5) + (0.5 × 0.5 × 0.5 × 0.5 × 0.5) + (0.5 × 0.5 × 0.5 × 0.5 × 0.5) + (0.5 × 0.5 × 0.5 × 0.5 × 0.5) + (0.5 × 0.5 × 0.5 × 0.5 × 0.5)

= 0.03125 + 0.03125 + 0.03125 + 0.03125 + 0.03125

= 0.15625

= 15.625%