let $m$ and $n$ be two events such that $p(m) = 0.24$ and $p(n) = 0.69$.
do not round your responses. (if necessary, consult a list of formulas.)

(a) determine $p(m \cup n)$, given that $m$ and $n$ are mutually exclusive.

(b) determine $p(m \cup n)$, given that $m$ and $n$ are independent.

Question

let $m$ and $n$ be two events such that $p(m) = 0.24$ and $p(n) = 0.69$.
do not round your responses. (if necessary, consult a list of formulas.)

(a) determine $p(m \cup n)$, given that $m$ and $n$ are mutually exclusive.

(b) determine $p(m \cup n)$, given that $m$ and $n$ are independent.

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Mutually Exclusive Events", "Independent Events Probability", "Addition Rule of Probability" ], "new_concepts": [], "current_concepts": [ "Mutually Exclusive Events", "Independent Events Probability", "Addition Rule of Probability" ] } ## Calculate union for mutually exclusive events Using the *Mutually Exclusive Events* and *Addition Rule of Probability* knowledge points $$ \begin{aligned} P(M \cap N) &= 0 \ P(M \cup N) &= P(M) + P(N) \ P(M \cup N) &= 0.24 + 0.69 = 0.93 \end{aligned} $$ ## Calculate union for independent events Using the *Independent Events Probability* and *Addition Rule of Probability* knowledge points $$ \begin{aligned} P(M \cap N) &= P(M) \times P(N) \ P(M \cap N) &= 0.24 \times 0.69 = 0.1656 \ P(M \cup N) &= P(M) + P(N) - P(M \cap N) \ P(M \cup N) &= 0.24 + 0.69 - 0.1656 = 0.7644 \end{aligned} $$ ## Question (a) $0.93$ ## Question (b) $0.7644$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Probability of Events" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate union for mutually exclusive events

Calculate union for independent events

Answer:

Question (a)

Question (b)