On a quiz with 10 multiple choice questions

Jelly Ksn

Jelly Ksn

Answered question

2022-07-04

On a quiz with 10 multiple choice questions each with 4 possible answers, find the probability of scoring at least
60% if you guess all the answers. Round your final answer to 4 decimal places.

Answer & Explanation

Vasquez

Vasquez

Expert2023-05-29Added 669 answers

To calculate the probability of scoring at least 60% on a quiz with 10 multiple-choice questions, each with 4 possible answers, when guessing all the answers, we need to consider the different possible outcomes and determine the favorable outcomes.
For each question, there are 4 possible answers, so the probability of guessing the correct answer by chance is 1/4.
To find the probability of scoring at least 60%, we need to consider the number of correct answers needed. Since 60% of 10 questions is 6 questions, we need to calculate the probability of getting 6, 7, 8, 9, or 10 questions correct.
Let's calculate the probability of getting exactly 6 questions correct:
P(6 correct)=(106)×(14)6×(34)4
Similarly, we can calculate the probabilities for 7, 8, 9, and 10 questions correct:
P(7 correct)=(107)×(14)7×(34)3
P(8 correct)=(108)×(14)8×(34)2
P(9 correct)=(109)×(14)9×(34)1
P(10 correct)=(1010)×(14)10×(34)0
Now, we can calculate the probability of scoring at least 60% by summing up these probabilities:
P(at least 60%)=P(6 correct)+P(7 correct)+P(8 correct)+P(9 correct)+P(10 correct)
Rounding the final answer to 4 decimal places will depend on the calculated probabilities.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?