Question

A student 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?

Answer 1

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

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

FTTTT or TFTTT or TTFTT or TTTFT or TTTTF

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%