Question

josiah takes a multiple-choice quiz that has three questions. each question has five answer options. if he randomly chooses his answers, what is the probability that he will get all three correct?
○ \\(\frac{1}{8}\\)
○ \\(\frac{1}{25}\\)
○ \\(\frac{1}{125}\\)
○ \\(\frac{1}{243}\\)

Explanation:

Step1: Probability of one correct answer

Each question has 5 options, so the probability of getting one question correct by random choice is $\frac{1}{5}$.

Step2: Probability of three correct answers

Since the choices for each question are independent events, we multiply the probabilities of getting each question correct. So for three questions, the probability is $(\frac{1}{5}) \times (\frac{1}{5}) \times (\frac{1}{5}) = \frac{1}{125}$.

Answer:

$\frac{1}{125}$ (corresponding to the option $\frac{1}{125}$)