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mathmath333

  • one year ago

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  1. mathmath333
    • one year ago
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    One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent? i.)E : ‘the card drawn is a king or queen’ F : ‘the card drawn is a queen or jack’.

  2. triciaal
    • one year ago
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    |dw:1439916492853:dw|

  3. mathmath333
    • one year ago
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    how do i calculate \(P(K\cap Q)\)

  4. mathmath333
    • one year ago
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    P(K\(\cup\)Q)=P(K)+P(Q)-P(K\(\cap\)Q)

  5. triciaal
    • one year ago
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    first let me remind you I am not the best stats person

  6. triciaal
    • one year ago
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    |dw:1439917813910:dw|

  7. anonymous
    • one year ago
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    Events are independent if one does not affect the other.

  8. freckles
    • one year ago
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    \[(\text{Q} \text{ or } \text{K}) \text{ and } (\text{Q} \text{ or } \text{J}) \\ =Q \text{ or } (K \text{ and } J) \text{ by distributive law }\\ =Q \text{ or } \emptyset \text{ since a card cannot be both a king and a jack} \\ = Q \] to check this one to see if it is independent you can see if the following equality holds: \[P((\text{Q} \text{ or } K) \text{ and } (\text{Q} \text{ or } \text{J}))=P(\text{Q} \text{ or } \text{K}) \cdot P(\text{Q} \text{ or } \text{J}) \\ \\ \text{ we know the left hand side just equals } P(\text{Q}) \\ \\ \text{ and we know } P(\text{Q})=\frac{4}{52}=\frac{1}{13} \\ \text{ so check to see if the right hand side is also } \frac{1}{13}\]

  9. freckles
    • one year ago
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    you should see it is not by what was worked out above

  10. freckles
    • one year ago
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    if the equality holds then E and F are independent if the equality fails then E and F aren't independent

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