if you make guesses for four multiple-choice test questions (each with five possible answers), what is the probability of getting at least one correct?
prob(right) = 1/5
prob(wrong) = 4/5
prob(at least one correct)
----> exclude the case of all wrong
prob(all wrong ) = (4/5)^4
prob(at least one right ) = 1 - (4/5)^4
= 369/625
To calculate the probability of getting at least one correct answer when making random guesses, we can first calculate the probability of getting none correct and then subtract it from 1.
For each question, there are five possible answers, so the probability of guessing the incorrect answer for a single question is 4/5 (since there is one correct answer and four incorrect ones). Thus, the probability of guessing all four questions incorrectly is:
(4/5) * (4/5) * (4/5) * (4/5) = 0.4096
Now, to find the probability of getting at least one correct answer, we subtract the probability of getting none correct from 1:
1 - 0.4096 = 0.5904
Therefore, the probability of getting at least one correct answer is approximately 0.5904, or 59.04%.