finding a probability

the probability of event a is 0.48, the probability of event a and b is 0.21, and the probability of events a or b is 0.89. what is the probability of event b?

0.09
0.20
0.27
0.62

Question

finding a probability

the probability of event a is 0.48, the probability of event a and b is 0.21, and the probability of events a or b is 0.89. what is the probability of event b?

0.09
0.20
0.27
0.62

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": [ "Probability Addition Rule" ], "new_concepts": [], "current_concepts": [ "Probability Addition Rule" ] } ## Identify the given values Using the *Probability Addition Rule* knowledge point $$ \begin{aligned} P(A) &= 0.48 \ P(A \cap B) &= 0.21 \ P(A \cup B) &= 0.89 \end{aligned} $$ ## Apply the Probability Addition Rule Using the *Probability Addition Rule* knowledge point $$ \begin{aligned} P(A \cup B) &= P(A) + P(B) - P(A \cap B) \ 0.89 &= 0.48 + P(B) - 0.21 \end{aligned} $$ ## Solve for the probability of event B Using the *Probability Addition Rule* knowledge point $$ \begin{aligned} 0.89 &= 0.27 + P(B) \ P(B) &= 0.89 - 0.27 \ P(B) &= 0.62 \end{aligned} $$

(A) 0.09

(B) 0.20

(C) 0.27

(D) 0.62

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

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Apply the Probability Addition Rule

Solve for the probability of event B

Answer: