In addition to his social studies class, Edward must complete a five question multiple-choice exam....

Step 1
Given,
Total number of questions ${\displaystyle =5}$
Probability of success ${\displaystyle =\frac{1}{4}}$ ( since each question has only 1 correct choice out of 4 choices)
We use binomial distribution here.
Step 2
(a) The probability that he will answer all five questions correctly:
${\displaystyle P(X=5)=5C_5{\left(\frac{1}{4}\right)}^5{(1-\frac{1}{4})}^{5-5}}$
${\displaystyle =0.000977}$
(b) The probability that he will answer exactly 2 questions correctly:
${\displaystyle P(X=2){=}^5{C}_2{\left(\frac{1}{4}\right)}^2{(1-\frac{1}{4})}^{5-2}}$
${\displaystyle =0.26367}$
(c) The probability that he will answer at least 2 questions correctly:
${\displaystyle P(X\ge 2)=1-P\left(X<2\right)}$
${\displaystyle =1-P(X=0)+P(X=1)}$
${\displaystyle =1-[0.2373+0.3955]}$
${\displaystyle =1-0.6328}$
${\displaystyle =0.3672}$

Step 1
a) The probability that Edward will answer all the six questions correctly is,
$P\text{(Six correct answers)}=((6),(6))(\frac{1}{4}{)}^6(\frac{3}{4}{)}^0$
${\displaystyle \approx 0.0002}$

Step 2
Thus, the probability that Edward will answer all the six questions correctly is 0.0002.
b) The probability that Edward will answer exactly two questions correctly is,
${\displaystyle P\text{(Two correct answers)}=\left(\begin{array}{c}6\\ 2\end{array}\right){\left(\frac{1}{4}\right)}^2{\left(\frac{3}{4}\right)}^4}$
${\displaystyle \approx 0.2966}$
Step 3
Thus, the probability that Edward will answer exactly two questions correctly is 0.2966.
c) The probability that Edward will answer at least two questions correctly is,
${\displaystyle P\text{(At least two correct answers)}=P(X\ge 2)}$
${\displaystyle =1-P\left(X<2\right)}$
${\displaystyle =1-P(X\le 1)}$
${\displaystyle =1-[P(X=0)+P(X=1)]}$
${\displaystyle =1-(0.1780+0.3560)}$
${\displaystyle =0.4660}$
Thus, the probability that Edward will answer at least two questions correctly is 0.4660.

I think the answer is c, at least three questions are correct, because he cannot answer everything correctly, and he cannot get the perfect number, 3.