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

Answer 2

The probability that the first question she gets right is the 5th question is 7.91%, the probability she gets all of the questions right is 0.09%, and the probability she gets at least one question right is 76%.

Given that in a multiple choice exam, there are 5 questions and 4 choices for each question, and Nancy has not studied for the exam at all and decides to randomly guess the answers, to determine what is the probability that: (A) the first question she gets right is the 5th question, (B) she gets all of the questions right, and (C) she gets at least one question right, the following calculations must be performed:

Since there are 4 possible options per question, the probability of getting each one right is 25%.

• A) 0.75 x 0.75 x 0.75 x 0.75 x 0.25 = X
• 0.0791 = X
• 7.91%

• B) 0.25 x 0.25 x 0.25 x 0.25 x 0.25 = X
• 0.0009 = X
• 0.09%

• C) 1 - (3/4) ^ 5 = X
• 1 - 0.23 = X
• 0.76 = X
• 76%

Thus, the probability that the first question she gets right is the 5th question is 7.91%, the probability she gets all of the questions right is 0.09%, and the probability she gets at least one question right is 76%.

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