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Thread: Rolling Dice/Drawing cards

  1. #1
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    Rolling Dice/Drawing cards

    In Exercises 15 to 20, two dice are rolled. Determine the
    probability of each of the following. (“Doubles” means that
    both dice show the same number.)

    17. Rolling an even number or doubles

    In Exercises 21 to 26, a single card is drawn from a
    standard deck. Find the probability of each of the following
    events.

    18. Drawing a diamond or a black card
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    Re: Rolling Dice/Drawing cards

    Quote Originally Posted by racertaz01 View Post
    In Exercises 15 to 20, two dice are rolled. Determine the
    probability of each of the following. (“Doubles” means that
    both dice show the same number.)
    17. Rolling an even number or doubles

    In Exercises 21 to 26, a single card is drawn from a
    standard deck. Find the probability of each of the following
    events.
    18. Drawing a diamond or a black card
    #17 is poorly stated. It says rolling an even number. Does that mean an even sum or does it mean an even number on at least one of the dice? I suspect it means SUM but have no way of knowing. Here is the outcome table:
    \begin{array}{*{20}{c}}{(1,1)}&{(1,2)}&{(1,3)}&{(1  ,4)}&{(1,5)}&{(1,6)}\\{(2,1)}&{(2,2)}&{(2,3)}&{(2,  4)}&{(2,5)}&{(2,6)}\\{(3,1)}&{(t3,2)}&{(3,3)}&{(3,  4)}&{(3,5)}&{(3,6)}\\{(4,1)}&{(4,2)}&{(4,3)}&{(4,4  )}&{(4,5)}&{(4,6)}\\{(5,1)}&{(5,2)}&{(5,3)}&{(5,4)  }&{(5,5)}&{(5,6)}\\{(6,1)}&{(6,2)}&{(6,3)}&{(6,4)}  &{(6,5)}&{(6,6)}\end{array}
    Now you can use those to simply count the positive outcomes.

    #18 $\mathcal{P}(D\cup B)=\mathcal{P}(D)+\mathcal{P}( B)-\mathcal{P}(D\cap B)$
    One of those is zero. WHY?
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    Re: Rolling Dice/Drawing cards

    All "doubles" sum to an even number so "doubles or an even number" is exactly the same as "an even number".

    "Diamonds" are red cards so "diamonds" and "black cards" are "mutually exclusive".
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