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Math Help - Data help

  1. #1
    Junior Member
    Joined
    Sep 2006
    Posts
    38

    Data help

    I'm doing some data hwk and i got stuck at these, can anyone go about showing me how to solve these?

    1) A Euchre deck has 24 cards: 9's, 10's, jacks, queens, kings, and aces from each of the four suits. If you were to deal out 5 cards from the deck, what is the probability that there would be a 10, jack, queen, king, and ace all from the same suit?

    2) How many paths will spell pascal? ...i just realized that this isn't showing up the way i want it to when i post but it goes out like a triangle up to the C and then it closes back like a diamond
    P
    A A
    S S S
    C C C C
    A A A
    L L

    I did this and i got 20 but i'm not sure if i'm right

    3) A dart board contains 20 equal-sized sectors numbers 1 to 20. A dart is ramdomly tossed at the board 10 times. what is the probability that that dart lands in the sector labled 20 a total of 5 times.

    I tried question 3 and i did this, can anyone tell me if i'm right?
    (10C5)*[(1/20)^5]*[(19/20)^5)

    Thanks
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
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    Hello, imthatgirl!

    1) A Euchre deck has 24 cards: 9's, 10's, J's, Q's, K's, and A's from each of the four suits.
    If you were to deal out 5 cards from the deck, what is the probability that
    there would be a 10, jack, queen, king, and ace all from the same suit?

    There are: . {24\choose5} \:=\:42,504 possible hands.

    There are exactly 4 Royal Flushes.

    Therefore: . P(\text{Royal Flush}) \;=\;\frac{4}{42.504} \;=\;\frac{1}{10,626}



    2) How many paths will spell PASCAL?
    Code:
                      P
                    /   \
                  A       A
                /   \   /   \
              S       S       S
            /   \   /   \   /   \
          C       C       C       C
            \   /   \   /   \   /
              A       A       A
                \   /    \   /
                  L        L
    I'll let someone else work on this one . . .



    3) A dart board contains 20 equal-sized sectors numbers 1 to 20.
    A dart is ramdomly tossed at the board 10 times.
    What is the probability that that dart lands in sector "20" exactly 5 times?

    I tried question 3 and i did this, can anyone tell me if i'm right?
    . {10\choose5}\left(\frac{1}{20}\right)^5\left(\frac  {19}{20}\right)^5 . . . . Yes!

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