Questions: What is the P(B)? Round to the 100ths place.

Transcript text: What is the $P(B)$ ? Round to the 100 ths place.

Solution

Solution Steps

Step 1: Identify the Given Probabilities

From the Venn diagram:

P(A) = 0.43
P(A ∩ B) = 0.04

Step 2: Use the Formula for the Union of Two Events

The formula for the union of two events is: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Step 3: Solve for P(B)

Rearrange the formula to solve for P(B): \[ P(B) = P(A \cup B) - P(A) + P(A \cap B) \]

Step 4: Substitute the Known Values

From the Venn diagram, the total probability (P(A ∪ B)) is 1 (since it represents the entire sample space): \[ P(B) = 1 - P(A) + P(A \cap B) \] \[ P(B) = 1 - 0.43 + 0.04 \]

Step 5: Calculate P(B)

\[ P(B) = 0.61 \]

Final Answer

\[ P(B) = 0.61 \]

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