What is the probability of getting five or fewer questions correct if guessing on all answers? (Round your answer to four decimal places.)
I have attempted to use the formula for binomial distribution and inputted $C(7,5)(1/5)^5(4/5)^2$, but I am provided $336/78125$ or $.0043$, and this is incorrect. I have also tried using simple logic that if $5$ are correct or fewer then at least $2$ have to be incorrect, so $4/5 \cdot 4/5 = 16/25 - 1 = 9/25 = .36$, and that is incorrect. Any guidance for a different approach is needed. I know it's simple but I feel like I've hit a wall.
The probability of getting all 7 answers correct is $(\frac{1}{5})^7$.
The probability of getting only 1 answer wrong would be $7 \cdot (\frac{1}{5})^6 \frac{4}{5}$
Therefore the probability of getting 5 answers or less correct would be $1- (\frac{1}{5})^7 - 7 \cdot (\frac{1}{5})^6 \frac{4}{5}$