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: Find probability of one - question correct

The probability of getting one question correct when there are 5 answer options is $\frac{1}{5}$ since there is 1 correct option out of 5.

Step2: Use multiplication rule for independent events

Since the questions are independent, the probability of getting all 3 questions correct is the product of the probabilities of getting each question correct. So we multiply $\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}$.
$\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}=\frac{1}{125}$

Answer:

$\frac{1}{125}$