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?

(a) $\frac{1}{8}$
(b) $\frac{1}{25}$
(c) $\frac{1}{125}$
(d) $\frac{1}{243}$

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?

(a) $\frac{1}{8}$
(b) $\frac{1}{25}$
(c) $\frac{1}{125}$
(d) $\frac{1}{243}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Theoretical Probability", "Independent Events", "Probability Multiplication Rule" ], "new_concepts": [], "current_concepts": [ "Theoretical Probability", "Independent Events", "Probability Multiplication Rule" ] } ## Determine the probability of a single correct guess Using the *Theoretical Probability* knowledge point $$ P(\text{Correct}) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{1}{5} $$ ## Apply the multiplication rule for independent events Using the *Independent Events* and *Probability Multiplication Rule* knowledge points $$ \begin{aligned} P(\text{All 3 Correct}) &= P(\text{Correct}) \times P(\text{Correct}) \times P(\text{Correct}) \ &= \frac{1}{5} \times \frac{1}{5} \times \frac{1}{5} \ &= \frac{1}{125} \end{aligned} $$

(A) $\frac{1}{8}$

(B) $\frac{1}{25}$

(C) $\frac{1}{125}$

(D) $\frac{1}{243}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Probability Multiplication Rule" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the probability of a single correct guess

Apply the multiplication rule for independent events

Answer: