question 14 points 3

you toss a fair coin three times. given that you have observed at least one tails, what is the probability that you observe at least two tails?

$\frac{4}{7}$

$\frac{3}{7}$

Question

question 14 points 3

you toss a fair coin three times. given that you have observed at least one tails, what is the probability that you observe at least two tails?

$\frac{4}{7}$

$\frac{3}{7}$

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": [ "Conditional Probability" ], "new_concepts": [], "current_concepts": [ "Conditional Probability", "Simple Events" ] } ## Identify the sample space Using the **Conditional Probability** knowledge point $$ S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\} $$ $$ |S| = 2^3 = 8 $$ ## Define the given condition Using the **Conditional Probability** knowledge point $$ \begin{aligned} A &= \{\text{at least one tails}\} \ &= \{HHT, HTH, THH, HTT, THT, TTH, TTT\} \ |A| &= 7 \end{aligned} $$ ## Define the target event Using the **Conditional Probability** knowledge point $$ \begin{aligned} B &= \{\text{at least two tails}\} \ &= \{HTT, THT, TTH, TTT\} \ |B| &= 4 \end{aligned} $$ ## Calculate the conditional probability Using the **Conditional Probability** knowledge point $$ \begin{aligned} B \cap A &= \{\text{at least two tails}\} \cap \{\text{at least one tails}\} \ &= \{HTT, THT, TTH, TTT\} \ |B \cap A| &= 4 \ P(B|A) &= \frac{|B \cap A|}{|A|} = \frac{4}{7} \end{aligned} $$

(A) $\frac{4}{7}$

(B) $\frac{3}{7}$

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

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QUESTION IMAGE

Question

Explanation:

Identify the sample space

Define the given condition

Define the target event

Calculate the conditional probability

Answer: