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Neep help in the sample space:

  1. Jun 19, 2004 #1
    1. Suppose that two cards are dealt from a standard 52-card poker deck. Let A be the event that the sum of the two cards is 8 (assume that aces have a numerical value of 1). How many outcomes are in A?

    Where I got stuck [WIGS]: Are the suits important here? So, there are a lot of outcomes then if repetition of value is permitted... How do I define my "outcomes" here... say 2 of hearts and 6 of diamonds?

    2. Consider the experiment of choosing coefficients for the quadratic equation ax^2 + bx + c = 0. Characterize the values of a, b and c associated with the event A: Equation has complex roots.

    [WIGS]: I don't get it well in a sense that I had hard time making a "set" out of the problem... I know that complex roots will occur of b^2 - 4ac < 0.
    How will I answer it - I mean, I only need to characterize my answer?

    3. A probability-minded despot offers a convicted murder a final chance
    to gain his release. The prisoner is given 20 chips, 10 white and 10 black. All 20 are to be placed in the two urns, according to the allocation scheme the prisoner wants, provided that each urn has at least 1 chip in it. The executioner will then pick one of the two urns at random, and from that urn, one chip at random. If the chip selected is white, the prisoner's free, otherwise, he "buys the farm". Characterize the sample space describing the prisoner's possible allocation options. (intuitively, which allocation affords the prisoner the greatest chance of survival?)

    [WIGS]: Do I have to list all his possible options? If yes, How will I define my elements to be used? If not, then I'm answering that enclosed in ()?
    What could be that greatest chance?


    -> I have my ideas but I'm not convinced yet on my own because
    these doubts make me uncertain.
     
  2. jcsd
  3. Jun 19, 2004 #2
    1. Suit only matters in that it distinguishes one card from another. So a 6 of spades and a 2 of diamonds would be different than a 6 of spades and a 2 of hearts.

    2. I'd describe the region by making a 3d graph. Let a = x, b = y, c = z and graph the region described by the inequality b^2 - 4ac < 0.

    3. Consider the extreme cases. 1 chip in one pot and 19 in the other and 10 chips in each pot. It'll be one of the two. Calculate the probability of not buying the farm for each.

    cookiemonster
     
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