Question 7 | BetaMath

Question 7

A driver’s knowledge test contains 30 multiple-choice questions, each with 4 options. An applicant must get at least 29 correct to pass.

If an applicant correctly answers the first 25 questions and randomly guesses the last 5 questions, what is the probability that the applicant will pass the test?

A. $\displaystyle \frac1{256}$

B. $\displaystyle \frac{15}{1024}$

C. $\displaystyle \frac1{64}$

D. $\displaystyle \frac{21}{256}$

Solution

To pass the test, the applicant must guess at least 4 of the 5 remaining questions correctly. Since each question is being answered randomly, the probability of answering any individual question correctly is $\displaystyle \frac14$ .

The probability of guessing all five answers correctly is equal to $\left(\frac14\right)^5$

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