you randomly select an integer from 0 to 9 (inclusively) and then randomly select an integer from 0 to 24 (inclusively). what is the probability of selecting a 6 both times?

the probability is
(type an integer or a decimal. do not round.)

Question

you randomly select an integer from 0 to 9 (inclusively) and then randomly select an integer from 0 to 24 (inclusively). what is the probability of selecting a 6 both times?

the probability is
(type an integer or a decimal. do not round.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Simple Event", "Compound Event" ], "new_concepts": [ "Independent Events Probability", "Multiplication Rule for Probability" ], "current_concepts": [ "Simple Event", "Compound Event", "Independent Events Probability", "Multiplication Rule for Probability" ] } ## Determine the probability of the first selection Using the *Simple Event* knowledge point $$ \begin{aligned} &\text{Integers from } 0 \text{ to } 9 \text{ inclusive: } \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\} \ &\text{Total outcomes } (N_1) = 10 \ &\text{Favorable outcome: } \{6\} \ &P(\text{selecting } 6 \text{ first}) = \frac{1}{10} = 0.1 \end{aligned} $$ ## Determine the probability of the second selection Using the *Simple Event* knowledge point $$ \begin{aligned} &\text{Integers from } 0 \text{ to } 24 \text{ inclusive: } \{0, 1, 2, \dots, 24\} \ &\text{Total outcomes } (N_2) = 25 \ &\text{Favorable outcome: } \{6\} \ &P(\text{selecting } 6 \text{ second}) = \frac{1}{25} = 0.04 \end{aligned} $$ ## Calculate the joint probability of both independent events Using the *Compound Event* knowledge point $$ \begin{aligned} &P(\text{selecting } 6 \text{ both times}) = P(\text{selecting } 6 \text{ first}) \times P(\text{selecting } 6 \text{ second}) \ &P(\text{selecting } 6 \text{ both times}) = \frac{1}{10} \times \frac{1}{25} = \frac{1}{250} = 0.004 \end{aligned} $$ You randomly select an integer from 0 to 9 (inclusively) and then randomly select an integer from 0 to 24 (inclusively). What is the probability of selecting a 6 both times? The probability is 0.004 (Type an integer or a decimal. Do not round.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Probability of Independent Events" ] }

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Question

Explanation:

Determine the probability of the first selection

Determine the probability of the second selection

Calculate the joint probability of both independent events

Answer: