Question

Exercise 3.10. Guessing on an exam. While taking a probability exam, you come to three questions that you have no clue how to answer. You would have known the answers if you had taken the time to study the night before instead of going to a party, but you did not make a good life choice, and you vow to never party on a school night again if you fail this exam. Each question on the exam is multiple choice with the correct answer being either a, b, c, d, or e. (Your guesses are independent.) What is the probability that: a. you randomly guess the right answer to all three questions? b. you randomly guess the right answer to none of the three questions? c. you randomly guess the right answer to exactly one of the three questions? d. you randomly guess the right answer to exactly two of the three questions? e. Do the probabilities in parts a-d sum o 1?

Answer 1

here this is binomial distribution with parameter n=3 and p=probability of getting right answer =1/5 =0.2

a)

P(X=3)=³C₃(0.2)³(0.8)⁰ =0.008

b)

P(X=0)=³C₀(0.2)⁰(0.8)³ =0.512

c)

P(X=1)=³C₁(0.2)¹(0.8)² =0.384

d)

P(X=2)=³C₂(0.2)²(0.8)¹ =0.096

e) sum of above probabilities=0.008+0.512+0.384+0.096 =1