Question

calculating a probability
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 for one question

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

Step2: Probability for three independent questions

Since the questions are independent, we multiply the probabilities for each question. So for three questions, the probability is $\frac{1}{5} \times \frac{1}{5} \times \frac{1}{5} = \frac{1}{5^3} = \frac{1}{125}$.

Answer:

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