Every question have 4 options and any one of the option is correct.
P(guessed option is correct) = 1 / 4
P(guessed option is not correct) = 3 / 4
Probability(Atleast two out of 5 are correct) = P(2 are correct) + P(3 are correct) + P(4 are correct)
+ P(5 are correct)
P(2 are correct) = $_{2}^{5}\textrm{C} \left ( 1/4 \right )^{2} \left ( 3/4 \right )^{3}$
P(3 are correct) = $_{3}^{5}\textrm{C} \left ( 1/4 \right )^{3} \left ( 3/4 \right )^{2}$
P(4 are correct) = $_{4}^{5}\textrm{C} \left ( 1/4 \right )^{4} \left ( 3/4 \right )^{1}$
P(5 are correct) = $_{5}^{5}\textrm{C} \left ( 1/4 \right )^{5} \left ( 3/4 \right )^{0}$
Probability(Atleast two out of 5 are correct) =
$_{2}^{5}\textrm{C} \left ( 1/4 \right )^{2} \left ( 3/4 \right )^{3}$ + $_{3}^{5}\textrm{C} \left ( 1/4 \right )^{3} \left ( 3/4 \right )^{2}$ + $_{4}^{5}\textrm{C} \left ( 1/4 \right )^{4} \left ( 3/4 \right )^{1}$ + $_{5}^{5}\textrm{C} \left ( 1/4 \right )^{5} \left ( 3/4 \right )^{0}$
= $\sum_{k=2}^{5} \binom{5}{k} \left ( 1/4 \right )^{k} \left ( 3/4 \right )^{5-k}$
Option B, is Correct Answer.
