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If E and F are mutually exclusive, then ...

If E and F are mutually exclusive, then `P(E nn F)` is equal to __________(Fill in the Blank)

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To solve the question, we need to understand the concept of mutually exclusive events in probability. ### Step-by-Step Solution: 1. **Definition of Mutually Exclusive Events**: - Two events E and F are said to be mutually exclusive if they cannot occur at the same time. This means that if one event occurs, the other cannot. 2. **Understanding Intersection of Events**: - The intersection of two events, denoted as \( P(E \cap F) \), represents the probability that both events occur simultaneously. 3. **Analyzing the Given Events**: - Since E and F are mutually exclusive, it follows that there are no outcomes that are common to both events. Therefore, the intersection of E and F contains no elements. 4. **Calculating the Probability**: - Since the intersection \( E \cap F \) is empty (i.e., it contains no elements), the probability of the intersection is: \[ P(E \cap F) = 0 \] 5. **Final Answer**: - Thus, \( P(E \cap F) \) is equal to **0**.
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Knowledge Check

  • If A and B are mutually exclusive events, then P(A cap B) equals

    A
    0
    B
    `1/2`
    C
    1
    D
    `1/4`
  • If A and B are mutually exclusive events, then P(A cap B) equals

    A
    0
    B
    `1/2`
    C
    1
    D
    `1/4`
  • If the vents A and B be mutually exclusive, then P(A+B) will be equal to

    A
    `P(A)+P(B)`
    B
    `P(A)-P(B)`
    C
    `P(A).P(B)`
    D
    `P(A)//P(B)`
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