let $a$ and $c$ be two events such that $p(a) = 0.55$ and $p(c) = 0.21$.

do not round your responses. (if necessary, consult a list of formulas.)

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

(b) determine $p(a \cup c)$, given that $a$ and $c$ are independent.

Question

let $a$ and $c$ be two events such that $p(a) = 0.55$ and $p(c) = 0.21$.

do not round your responses. (if necessary, consult a list of formulas.)

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

(b) determine $p(a \cup c)$, given that $a$ and $c$ 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 $$ \begin{aligned} &P(A \cap C) = 0\ &P(A \cup C) = P(A) + P(C) = 0.55 + 0.21 = 0.76 \end{aligned} $$ ## Calculate union for independent events Using the *Independent Events Probability* and *Addition Rule of Probability* knowledge points $$ \begin{aligned} &P(A \cap C) = P(A) \cdot P(C) = 0.55 \cdot 0.21 = 0.1155\ &P(A \cup C) = P(A) + P(C) - P(A \cap C) = 0.55 + 0.21 - 0.1155 = 0.6545 \end{aligned} $$ ## Question a $P(A \cup C) =$ 0.76 ## Question b $P(A \cup C) =$ 0.6545 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Statistics", "Probability of Events" ] }

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Question

Explanation:

Calculate union for mutually exclusive events

Calculate union for independent events

Answer:

Question a

Question b