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?
Options:
- One-eighth
- One-twenty-fifth
- [tex]\(\frac{1}{125}\)[/tex]
- [tex]\(\frac{1}{243}\)[/tex]
Answer (2)
The probability that Josiah randomly guesses all three questions correctly on the quiz is 125 1 . Therefore, the chosen option is 125 1 .
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To determine the probability that Josiah will get all three questions correct on a multiple-choice quiz, we follow these steps:
Identify the probability of getting a single question correct:
Each question has 5 answer choices, and only one of these choices is correct. Therefore, the probability of guessing the correct answer for one question is 5 1 .
Calculate the probability of getting all three questions correct:
Each question is independent, meaning the outcome of one question does not affect the others. Therefore, to find the probability of all three answers being correct, we multiply the probability of each question being answered correctly:
( 5 1 ) × ( 5 1 ) × ( 5 1 ) = ( 5 1 ) 3 = 125 1
Conclusion:
The probability that Josiah will randomly guess and get all three questions correct is 125 1 .
Therefore, the correct multiple-choice option is: 125 1 .
