Question

calculate the probability of randomly guessing at least 7 correct answers on a 10 questions true or false quiz to get a passing grade?

Answer 1

Remember the probability of k successes in a binomial trial
\[
g(k)=P[X=k]= \frac {n!}{k! \, (n-k)!} p^k (1-p)^{n-k}
\]
Here
\[
p=q=1/2;
\]

Answer 2

So in this case
\[
g(k) =\frac 1 {2^{10}} \frac {10!}{k! (10 -k)!}
\]
The answer should be
\[
g(7)+g(8)+g(9) + g(10)
\]

Answer 3

\[

\frac{15}{128}+ \frac{45}{1024}+ \frac{5}{512}+ \frac{1}{1024} =\frac{11}{64}
\]