In a sample space S, the two events A,B are such that P(A) = .6, P(B) = .2, P((AN B)c) = .9. What is P(An B)? Ο ΡΑB) 6 O P(AN B) = .1 (answer) O P(AN B) = .12 Ο Ρ(An B ) -0 In a sample space S, the two events A,B are such that P(A) = .6, P(B) = .2, P((An B)°) = .9. The events A and B are: O Mutually Exclusive O Independent O Neither Mutually Exclusive nor Independent (answer) O Both Mutually Exclusive and Independent

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**Problem 1: Probability of Intersection**

In a sample space \( S \), the two events \( A, B \) are such that \( P(A) = 0.6 \), \( P(B) = 0.2 \), \( P((A \cap B)^c) = 0.9 \). What is \( P(A \cap B) \)?

- \( \bigcirc \) \( P(A \cap B) = 0.6 \)
- \( \bigcirc \) \( P(A \cap B) = 0.1 \) (answer)
- \( \bigcirc \) \( P(A \cap B) = 0.12 \)
- \( \bigcirc \) \( P(A \cap B) = 0 \)

**Problem 2: Relationship of Events**

In a sample space \( S \), the two events \( A, B \) are such that \( P(A) = 0.6 \), \( P(B) = 0.2 \), \( P((A \cap B)^c) = 0.9 \). The events \( A \) and \( B \) are:

- \( \bigcirc \) Mutually Exclusive
- \( \bigcirc \) Independent
- \( \bigcirc \) Neither Mutually Exclusive nor Independent (answer)
- \( \bigcirc \) Both Mutually Exclusive and Independent
Transcribed Image Text:**Problem 1: Probability of Intersection** In a sample space \( S \), the two events \( A, B \) are such that \( P(A) = 0.6 \), \( P(B) = 0.2 \), \( P((A \cap B)^c) = 0.9 \). What is \( P(A \cap B) \)? - \( \bigcirc \) \( P(A \cap B) = 0.6 \) - \( \bigcirc \) \( P(A \cap B) = 0.1 \) (answer) - \( \bigcirc \) \( P(A \cap B) = 0.12 \) - \( \bigcirc \) \( P(A \cap B) = 0 \) **Problem 2: Relationship of Events** In a sample space \( S \), the two events \( A, B \) are such that \( P(A) = 0.6 \), \( P(B) = 0.2 \), \( P((A \cap B)^c) = 0.9 \). The events \( A \) and \( B \) are: - \( \bigcirc \) Mutually Exclusive - \( \bigcirc \) Independent - \( \bigcirc \) Neither Mutually Exclusive nor Independent (answer) - \( \bigcirc \) Both Mutually Exclusive and Independent
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