Question

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that: (a) the first question she gets right is the 5th question? (b) she gets all of the questions right? (c) she gets at least one question right?

Answer 1

Answer: a) 0.07910, b) 0.000976, c) 0.7626

Step-by-step explanation:

Since we have given that

Number of questions = 5

Number of choices = 4

P(getting correct) = $\dfrac{1}{4}=0.25$

a) the first question she gets right is the 5th question?

P(getting 4 wrongs answers and one right answer) is given by

$(1-0.25)^4\times 0.25\\\\=0.75^4\times 0.25\\\\=0.07910$

b) she gets all of the questions right?

P(all right )= $0.25^5=0.000976$

c) she gets at least one question right?

1-P(All of them wrong)

$=1-(1-0.25)^5\\\\=1-0.7565\\\\=1-0.2373\\\\=0.7626$

Hence, a) 0.07910, b) 0.000976, c) 0.7626