if two events a and b are dependent, the probability of both occurring is:

$p(a \text{ and } b) = p(a) + p(b)$
$p(a \text{ and } b) = p(a) \times p(a \text{ given } b)$
$p(a \text{ and } b) = p(a) \times p(b \text{ given } a)$
$p(a \text{ and } b) = p(a) \times p(b)$

Question

if two events a and b are dependent, the probability of both occurring is:

$p(a \text{ and } b) = p(a) + p(b)$
$p(a \text{ and } b) = p(a) \times p(a \text{ given } b)$
$p(a \text{ and } b) = p(a) \times p(b \text{ given } a)$
$p(a \text{ and } b) = p(a) \times p(b)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Dependent Events" ], "new_concepts": [], "current_concepts": [ "Dependent Events", "Conditional Probability" ] } ## Identify the multiplication rule for dependent events $$ P(A \text{ and } B) = P(A) \times P(B \mid A) $$ ## Match with the given options $$ P(A \text{ and } B) = P(A) \times P(B \text{ given } A) $$

P(A and B) = P(A) + P(B)

P(A and B) = P(A) x P(A given B)

P(A and B) = P(A) x P(B given A)

P(A and B) = P(A) x P(B)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Dependent Events" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the multiplication rule for dependent events

Match with the given options

Answer: