$$ \begin{array}{llll}37 & 38 & 39 & 40\end{array} $$ Current learning objective: The Addition Rule Question 30 Practice similar questions Score: 0 of 3 points Consider two events, $$ A $$ and $$ B $$, with the following probabilities: $$ \begin{array}{l} P(A)=0.56 \ P(B)=0.52 \ P(A \cap B)=0.3 \end{array} $$ Find the probability of $$ A \cup B $$. Round to the nearest hundredth as needed. $$ P(A \cup B)= $$ Enter your answer

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UpStudy AI · Accepted Answer

To find the probability of $$ A \cup B $$ (either event $$ A $$ **or** event $$ B $$ occurring), you can use the **Addition Rule**:

$$
P(A \cup B) = P(A) + P(B) - P(A \cap B)
$$

Given:
$$
P(A) = 0.56 \
P(B) = 0.52 \
P(A \cap B) = 0.3
$$

Plugging in the values:

$$
P(A \cup B) = 0.56 + 0.52 - 0.3 = 1.08 - 0.3 = 0.78
$$

**Answer:** 
$$
P(A \cup B) = 0.78
$$
$$ P(A \cup B) = 0.78 $$

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