2022-01-12

you are currently taking your multiple-choice file exam that contains 50 questions with 4 answer choices each using binomial probability what is the probability you get exactly 13 questions correct around your answer to the nearest thousandth

nick1337

Conditions are:

2. Each question has 4 options with only one correct answer and all other incorrect answers.
3. Student is equally likely to pick any outcome in any given question.
4. Hence, probability of choosing correct answer is $\frac{1}{4}=0.25$. Probability of choosing incorrect answer is $1-\frac{1}{4}=\frac{3}{4}=0.75$.
5. The number of trials is 50.
6. Total number of success is exactly 13 and failure is 37 amongst the 50 questions in any particular order.

Now, calculation is fairly simple.

Binomial probability distribution is such that…

P(13 correct ; 37 wrong)

$={C}_{13}^{50}×\left(0.25{\right)}^{13}×\left(0.75{\right)}^{37}$

$=\frac{44357564825\cdot {3}^{37}}{{2}^{97}}\approx 0.127$

Do you have a similar question?