Question

Round to 4 decimals please

A quiz has 12 multiple choice questions. Each question has 4 answer choices. If a student takes the quiz and randomly guesses on every question..

Question 1 Find the probability the student gets between 1 and 6, exclusive, questions correct?

Question 2 Find the probability the student gets more than 8 questions correct?

Answer 1

Solution:

The probability of k successes in n trials where is the probability of success on any given trial is given by:

Where is the number of combinations of things taken at a time and is calculated by

p = 0.25, n = 12
Question 1 :
P(1< X < 6) = P(X = 2) + P(X = 3) + P(X = 4 ) + P(X = 5)
= 0.2323 + 0.2581 + 0.1936 + 0.1032 = 0.7872

Question 2:
P(X > 8) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)
= 0.0003 + 0.0000 + 0.0000 + 0.0000
= 0.0003