Question

A student makes random guesses for 10 true/false questions. What is the probability of getting one correct answer?

Answer 1

Probability of at least one correct answer: `1023/1024`

Probability of exactly one correct answer: `5/512`

Explanation:

The probability of an event occurring can be calculated as

`"Number of ways the event can occur"/"Total possibilities"`

As there are two possible results for each of the ten questions, there are `2^10 = 1024` possibilities total. To calculate the probability, then, we only need to know how many ways the student can get one correct answer.

There is some slight ambiguity in the wording of the question, so we will address both interpretations.

Probability of at least one correct answer:

There is only one way the student can have no correct answers, meaning there are `1024-1=1023` ways the student can have at least one correct answer. Thus, the probability of getting at least one correct answer is `1023/1024~~0.999`

Probability of exactly one correct answer:

There are ten ways the student can get exactly one correct answer (one for each possible question they could have guessed correctly). Thus, the probability of getting exactly one correct answer is `10/1024=5/512~~0.010`