Stephens Santiago
08/11/2023 · Junior High School
What is the complement of guessing on 5 correct answers on a 5-question true/false exam?
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The complement of guessing on 5 correct answers on a 5-question true/false exam refers to the probability of not getting all 5 answers correct.
To find this, we first calculate the probability of getting all 5 answers correct by guessing. Since each question has 2 possible answers (true or false), the probability of guessing correctly for each question is \( \frac{1}{2} \). Therefore, the probability of getting all 5 questions correct is:
\[
P(\text{all correct}) = \left(\frac{1}{2}\right)^5 = \frac{1}{32}
\]
Now, the complement of this event (not getting all 5 correct) is:
\[
P(\text{not all correct}) = 1 - P(\text{all correct}) = 1 - \frac{1}{32} = \frac{31}{32}
\]
Thus, the complement of guessing on 5 correct answers on a 5-question true/false exam is \( \frac{31}{32} \).
Quick Answer
The complement is \( \frac{31}{32} \).
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