Questions: Use the given information to find the indicated probability. P(A)=0.1, P(B)=0.3, P(A ∩ B)=0.05. Find P(A ∪ B). P(A ∪ B)=

Use the given information to find the indicated probability. P(A)=0.1, P(B)=0.3, P(A ∩ B)=0.05. Find P(A ∪ B). P(A ∪ B)=
Transcript text: Use the given information to find the indicated probability. \[ \begin{array}{l} P(A)=0.1, P(B)=0.3, P(A \cap B)=0.05 . \text { Find } P(A \cup B) . \\ P(A \cup B)= \end{array} \]
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Solution

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Solution Steps

To find the probability of the union of two events \( A \) and \( B \), we can use the formula for the probability of the union of two events:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Given the probabilities \( P(A) = 0.1 \), \( P(B) = 0.3 \), and \( P(A \cap B) = 0.05 \), we can substitute these values into the formula to find \( P(A \cup B) \).

Step 1: Given Probabilities

We are given the following probabilities:

  • \( P(A) = 0.1 \)
  • \( P(B) = 0.3 \)
  • \( P(A \cap B) = 0.05 \)
Step 2: Apply the Union Formula

To find \( P(A \cup B) \), we use the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Step 3: Substitute Values

Substituting the given values into the formula: \[ P(A \cup B) = 0.1 + 0.3 - 0.05 \]

Step 4: Calculate the Result

Calculating the expression: \[ P(A \cup B) = 0.1 + 0.3 - 0.05 = 0.35 \]

Final Answer

Thus, the probability \( P(A \cup B) \) is \[ \boxed{0.35} \]

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