Probabilities

Question

Suppose an exam consisted of 10 multiple choice problems, each with five possible responses (A-E), only 1 of which is correct. If a student randomly guesses the answers to each question then what is the probability that a student guesses the correct answer to exactly 7 questions? Additionally, what is the probability that a student passes the exam with a score of 70% or higher? (round to 5 decimal places)

Answer 1

_nC_{r is the binomial coefficient of n things taken r at a time.}

 

Exactly 7 = ₁₀C_{7 * (.2)⁷ * (.8)³}

 

Score 70 or more = ∑₁₀C_{r *} (.2)^r * (.8)^10-r for r = 7 to 10