Question

an unprepared student makes random guesses for the ten true-false questions on a quiz. find the probability that there is at least one correct answer. express your answer as a decimal rounded to the third place.

Answer 1

The probability that there is at least one correct answer is 0.999 .

In a true-false quiz with 10 questions, there are two possible outcomes for each question: either a correct answer (C) or an incorrect answer (I).

The probability of getting a correct answer for a single question by random guessing is
`(1)/(2)`

​since there are two equally likely possibilities (true or false).

The probability of getting all answers incorrect in all 10 questions is

(
`(1)/(2)` )^10 , as the events are independent.

The probability of getting at least one correct answer is the complement of getting all answers incorrect.

So, the probability of getting at least one correct answer is 1 - (
`(1)/(2)` )^10 .

Let's calculate this:

P(at least one correct)=1−(
`(1)/(2)` )^10

P(at least one correct)= 1 -
`(1)/(1024)`

P(at least one correct)≈0.999

Rounded to the third decimal place, the probability is approximately 0.999.

Therefore, the probability that there is at least one correct answer is 0.999.