Answer: The probability of three correct answers and three incorrect answers is [tex]\frac{1}{64}[/tex]
Step-by-step explanation:
Since we have given that
There is a true - false quiz of six questions.
Probability of getting a true = [tex]\frac{1}{2}[/tex]
Probability of getting a false = [tex]\frac{1}{2}[/tex]
Probability that she answers the first three questions correctly and the last three questions incorrectly is given by
P(Three correct) × P(Three incorrect)
[tex](\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2})\times (\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2})\\\\=(\frac{1}{2})^6\\\\=\frac{1}{64}[/tex]
Hence, the probability of three correct answers and three incorrect answers is [tex]\frac{1}{64}[/tex]
