Question
If \( A, B \) are two events of the sample space of a random experiment and \( P(A)=0.7 \) \( , P(B)=0.3, P(A \cap B)=0.2 \), find : \( \begin{array}{l}\text { 1) The probability of occurrence of the event } A \text { only. } \\ \text { (2 } P(B) \\ \text { B } P(A \cup B)\end{array} \)
Ask by Donnelly Horton. in Egypt
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
- The probability of event \( A \) only is 0.5.
- The probability of event \( B \) is 0.3.
- The probability of either \( A \) or \( B \) occurring is 0.8.
Solution
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The Deep Dive
To find the probabilities: 1) The probability of occurrence of the event \( A \) only is given by \( P(A) - P(A \cap B) \): \[ P(A \text{ only}) = P(A) - P(A \cap B) = 0.7 - 0.2 = 0.5. \] 2) The probability of occurrence of event \( B \) is already given as: \[ P(B) = 0.3. \] 3) To find \( P(A \cup B) \), we can use the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.7 + 0.3 - 0.2 = 0.8. \] So, summarizing the results: 1) \( P(A \text{ only}) = 0.5 \) 2) \( P(B) = 0.3 \) 3) \( P(A \cup B) = 0.8 \)
