A multiple-choice test consists of five questions, each with A-E answers. If you guess the answer to each question, what is the probability of getting three or more questions correct?
A) 5.1%
B) 0.64%
C) 0.032%
D) 5.7%

Question

Quizplus · Accepted Answer

The probability of guessing a question correctly is 1/5, and incorrectly is 4/5. To find the probability of getting exactly three, four, or five questions correct, we use the binomial probability formula. Then, we sum these probabilities.For exactly three correct: $ \binom{5}{3} \left(\frac{1}{5}\right)^3 \left(\frac{4}{5}\right)^2 $For exactly four correct: $ \binom{5}{4} \left(\frac{1}{5}\right)^4 \left(\frac{4}{5}\right)^1 $For exactly five correct: $ \binom{5}{5} \left(\frac{1}{5}\right)^5 \left(\frac{4}{5}\right)^0 $Summing these probabilities gives us the total probability of getting three or more questions correct, which is approximately 5.7%.

A Multiple-Choice Test Consists of Five Questions, Each with A-E