In a multiple-choice quiz, there are 5 questions and 4 choices for each question (a, b, c, d). Robin has
not studied for the quiz at all, and decides to randomly guess the answers. What is the probability that:
a. the first question she gets right is the 3rd question?
b. she gets exactly 3 or exactly 4 questions right?
c. she gets the majority of the questions right?
Answers
Answer:
option c is correct
hope it will help you
a) probability that the first question she gets right is the 3rd question = 48/256
b) probability that she gets exactly 3 or exactly 4 questions right = 675/1024
c) probability that she gets the majority of the questions right = 918/1024
Probability of getting a question right = 1/4
Probability of getting a question wrong = 3/4
If she gets the first question right as the third question -
probability = (1/4 × 1/4 × 3/4 × 1/4 × 1/4) + (1/4 × 1/4 × 3/4 × 3/4 × 3/4) + (1/4 × 1/4 × 3/4 × 1/4 × 3/4) + (1/4 × 1/4 × 3/4 × 3/4 × 1/4)
=> 3/256 + 27/256 + 9/256 + 9/256
=> 48/256
If she gets exactly 3 or 4 questions right -
probability = 5C3 (3/4)³ (1/4)² + 5C4 (3/4)⁴ (1/4)
=> (10 × 27)/1024 + 405/1024
=> 675/1024
If she gets majority of the questions right -
probability = 5C3 (3/4)³ (1/4)² + 5C4 (3/4)⁴ (1/4) + 5C5 (3/4)^5
=> (10 × 27)/1024 + 405/1024 + 243/1024
=> 918/1024