g.pr.10.3 (mc)

$p(a) = 0.25$ and $p(a \cap b) = 0.175$. a and b are independent events. find $p(b)$.

- 0.7
- 0.075
- 0.01875
- 0.25

Question

g.pr.10.3 (mc)

$p(a) = 0.25$ and $p(a \cap b) = 0.175$. a and b are independent events. find $p(b)$.

- 0.7
- 0.075
- 0.01875
- 0.25

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Independent Events", "Probability Formulas" ], "new_concepts": [], "current_concepts": [ "Independent Events", "Probability Formulas" ] } ## State the formula for independent events $$ P(A \cap B) = P(A) \cdot P(B) $$ ## Substitute the given values and solve for P(B) $$ \begin{aligned} 0.175 &= 0.25 \cdot P(B) \ P(B) &= \frac{0.175}{0.25} \ P(B) &= 0.7 \end{aligned} $$

(A) 0.7

(B) 0.075

(C) 0.01875

(D) 0.25

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

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QUESTION IMAGE

Question

Explanation:

State the formula for independent events

Substitute the given values and solve for P(B)

Answer: