in a multiple choice test comprising 5 questions , each with 4 choices , what is the probability of a student getting 3 or more questions correct ? each question has only one correct answer and the student is equally likely to choose any of the 4 choices .  Choose the correct choice from the following answers:  A) 24 / 256  B) 53 / 512  C) 105 / 512  D) 459 / 512  E) 47 / 256

Rationale: probability for choosing correct answer is 1 / 4 and incorrect answer is 3 / 4 for 3 correct answers , c ( 5,3 ) * ( 1 / 4 ) ^ 3 * ( 3 / 4 ) ^ 2 = 90 / ( 4 ^ 5 ) for 4 correct answers , c ( 5,4 ) * ( 1 / 4 ) ^ 4 * ( 3 / 4 ) ^ 1 = 15 / ( 4 ^ 5 ) for 5 correct answers , c ( 5,5 ) * ( 1 / 4 ) ^ 5 * ( 3 / 4 ) ^ 0 = 1 / ( 4 ^ 5 ) so total probability = 106 / 1024 = 53 / 512 ans b
Answer: B