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Homework Help: Help with probability problems!

  1. Sep 22, 2010 #1
    1. The problem statement, all variables and given/known data
    1. Suppose we roll 10 fair 6-sided dice. What is the probability that there are exactly two 2's showing?
    2. Suppose we are dealt five cards from a standard 52-card deck. What is the probability that
    a) we get all 4 aces and the king of spades
    b) all 5 are spades
    c) we get no pairs (all are different values)
    d) a full house (3 of a kind and 2 of a kind)


    2. Relevant equations

    This one is correct:
    there are 2 pots
    in pot1 there is 5 red balls and 7 blue balls
    in pot2 there is 6 red balls and 12 blue balls
    3 balls are chosen randomely from each pot
    chances of all 6 balls to be same color = P(A)
    chances of all 6 balls to be red = P(B)
    chances of all 6 balls to be blue = P(C)

    P(A) = P(B or C)
    =P(B) + P(C) -0
    P(B)=|B|/|S| = |B|/(12choose3)(18choose3) =
    (5choose3)(7choose0)(6choose3)(12choose0)/(12choose3)(18choose3) = 5/4488
    P(C)=|C|/|S| = |C|/(12choose3)(18choose3) =
    (5choose0)(7choose3)(6choose0)(12choose3)/(12choose3)(18choose3) = 35/816
    P(A) = 5/4488 + 35/816 - 0 = 395/8976




    3. The attempt at a solution

    1.
    number of outcomes = 6^10 = 60466176
    10!/2!8! = 45
    so i get
    45/60466176

    2.
    number of outcomes = 52x51x50x49x48 / 5x4x3x2x1 = 2598960
    a) Here i have two different methods, i don't know if both are wrong or one is right...
    method 1
    (4choose1 * 4choose4 ) / 2598960 = 1/649740
    method 2
    ( (13choose1) * (13choose1) * (13choose1) * (13choose1) ) / 2598960 = ~0.066
    b)
    (13choose5)/2598960 = ~4.95x10^(-4)
    c)
    ( (4choose1)*(4choose1)*(4choose1)*(4choose1)*(4choose1) ) /2598960 = ~3.95x10^(-4)
    d)
    (4choose3)*(4choose2) /2598960 = 1/108290
     
  2. jcsd
  3. Sep 23, 2010 #2
    Let's look at (1) first. The number of ways to choose 2 of the 10 die to be rolled a 2 is 45, but that's not the total number of configurations in which exactly 2 die show a 2. Why not?
     
  4. Sep 23, 2010 #3
    I don't get how to complete it. I am too lost...
     
    Last edited: Sep 23, 2010
  5. Sep 23, 2010 #4
    anyone?
     
  6. Sep 23, 2010 #5
    I dont under stand what i am doing wrong
    i did
    10x9 / 2x1 = 45
    10x9 is because after i get one result theres 9 dice, and divinding it by 2! means i am removing all repeated sequences.
     
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