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.
A) $\frac { 9 } { 10 }$
B) $\frac { 1,023 } { 1,024 }$
C) $\frac { 1 } { 1,024 }$
D) $\frac { 1 } { 10 }$

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. 
A) $\frac { 9 } { 10 }$
B) $\frac { 1,023 } { 1,024 }$
C) $\frac { 1 } { 1,024 }$
D) $\frac { 1 } { 10 }$

Quizplus · Accepted Answer

The probability of guessing all questions wrong is $(\frac{1}{2})^{10} = \frac{1}{1024}$. Therefore, the probability of getting at least one correct is $1 - \frac{1}{1024} = \frac{1023}{1024}$.

An Unprepared Student Makes Random Guesses for the Ten True-False 910\frac { 9 } { 10 }109​

An Unprepared Student Makes Random Guesses for the Ten True-False $\frac { 9 } { 10 }$