question 8 of 10

a survey asked students whether they have any siblings and pets. the survey data are shown in the relative frequency table.

given that a student has a sibling, what is the likelihood that he or she does not have a pet?

a. 60%
b. 45%
c. 40%
d. about 82%

Question

question 8 of 10

a survey asked students whether they have any siblings and pets. the survey data are shown in the relative frequency table.

given that a student has a sibling, what is the likelihood that he or she does not have a pet?

a. 60%
b. 45%
c. 40%
d. about 82%

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Conditional Probability", "Two-Way Relative Frequency Tables" ], "new_concepts": [], "current_concepts": [ "Conditional Probability", "Two-Way Relative Frequency Tables" ] } ## Identify the given condition and target event $$ \begin{aligned} &\text{Condition } (A): \text{Student has a sibling (Siblings)} \ &\text{Target Event } (B): \text{Student does not have a pet (No pets)} \end{aligned} $$ ## Extract relative frequencies from the table $$ \begin{aligned} &P(\text{Siblings}) = 0.75 \ &P(\text{No pets} \cap \text{Siblings}) = 0.45 \end{aligned} $$ ## Calculate the conditional probability $$ \begin{aligned} &P(\text{No pets} \mid \text{Siblings}) = \frac{P(\text{No pets} \cap \text{Siblings})}{P(\text{Siblings})} \ &P(\text{No pets} \mid \text{Siblings}) = \frac{0.45}{0.75} = 0.6 = 60\% \end{aligned} $$

(A) 60%

(B) 45%

(C) 40%

(D) About 82%

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

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QUESTION IMAGE

Question

Explanation:

Identify the given condition and target event

Extract relative frequencies from the table

Calculate the conditional probability

Answer: