In a multiple choice test comprising 5 Questions, each with 4 choices

The probability of getting correct (C) answer is 1/4 and the the probability of getting wrong (W) answer is 3/4.

We need to find the probability of getting at 3, 4 or 5 correct answers:

The probability of getting 3 correct answers out of 5 is \(\frac{5!}{3!2!}*(\frac{1}{4})^3*(\frac{3}{4})^2\), we are multiplying by \(\frac{5!}{3!2!}\) since CCCWW scenario can occur in several ways: CCCWW, WWCCC, CWCWC, ... basically the number of permutations of 5 letters CCCWW, out of which 3 C's and 2 W's are identical (\(\frac{5!}{3!2!}\));

The probability of getting 4 correct answers out of 5 is \(\frac{5!}{4!}*(\frac{1}{4})^4*(\frac{3}{4})\);

The probability of getting 5 correct answers out of 5 is simply \((\frac{1}{4})^5\).

The overall probabity will be the sum of the above probabilities: \(\frac{5!}{3!2!}*(\frac{1}{4})^3*(\frac{3}{4})^2+\frac{5!}{4!}*(\frac{1}{4})^4*(\frac{3}{4})+(\frac{1}{4})^5=\frac{53}{512}\).

Answer: B.

P.S. Not a GMAT type of qustion.