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Anita505

  • 2 years ago

A card is drawn at random from a standard 52-card deck. Events G and H are: G= the drawn card is black H= the drawn card is divisible by 5 (face cards are not valued) (A)Find P(HIG) (B)Test H and G for independence (A)P(HIG)=

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  1. kropot72
    • 2 years ago
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    P(H|G) means the probability of H given G. Given that the drawn card is black, the sample space is 26 cards. There are 4 black cards that are either a 5 or a 10. \[P(H|G)=\frac{4}{26}=\frac{2}{13}\]

  2. kropot72
    • 2 years ago
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    @Anita505 Are you there?

  3. Anita505
    • 2 years ago
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    yes i am here :)

  4. Anita505
    • 2 years ago
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    Thank you for the help! @kropot72

  5. kropot72
    • 2 years ago
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    You're welcome :)

  6. Anita505
    • 2 years ago
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    however would Test H and G for independence... would it be independent? or dependent?

  7. Anita505
    • 2 years ago
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    oh its independent

  8. kropot72
    • 2 years ago
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    If two events A and B are independent, then the probability of A occurring is unaffected by whether of not B has occurred. Therefore if the events are independent P(A|B) = P(A) In this case we test whether P(H|G) = P(H) There are 8 cards that are 5 or 10 and either black or red. Therefore \[P(H)=\frac{8}{52}=\frac{2}{13}\] Have we confirmed that H and G are independent?

  9. Anita505
    • 2 years ago
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    Yes this is independent :) thank you once again for your help! much appreciated!

  10. kropot72
    • 2 years ago
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    Correct! You're welcome :)

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