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    zacissohot2's Avatar
    zacissohot2 Posts: 1, Reputation: 1
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    #1

    Apr 28, 2008, 08:03 PM
    probability for solving equations
    how do you solve this problem? Your sock drawer contains 3 pairs of gray socks, 4 pairs of white socks, 4 pairs of black socks, and 7 pairs of beige socks. You choose a pair of socks from the drawer at random and then replace it. Then you choose a second pair of socks. Find P[gray,thengray].
    BatteryHeights's Avatar
    BatteryHeights Posts: 6, Reputation: 2
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    #2

    Apr 28, 2008, 09:13 PM
    STEP 1:
    First, calculate P[gray], which represents the probability of pulling out a pair of gray socks on the first try. To do this, you just need to calculate the percentage of gray pairs in the drawer and then use the formula:

    (number pairs gray / number pairs total) * 100 [where / means divide and * means multiply]

    STEP 1-A:
    3 pairs gray + 4 pairs white + 4 pairs black + 7 pairs beige = 18 pairs in total

    STEP 1-B:
    3 pairs gray divided by 18 pairs total (or 3 / 18) = 0.166666667

    STEP 1-C:
    0.166666667 * 100 = 16.6666667% <-- this is P[gray] or the probability of pulling out a gray pair on the first try

    STEP 2:
    Next calculate P[gray, thengray], which represents the probability of pulling out a pair of gray socks on the first try and then again on the second try. To do this, you just need to multiply P[gray] by itself 2 times, because you want to calculate the probability of pulling out a gray pair 2 times in a row. Use this formula:

    P[gray] * P[gray]
    This can also be written as: "P[gray] squared" or "P[gray] to the second power"

    STEP 2-A:
    16.6666667% * 16.6666667% = 0.0277777779

    STEP 2-B:
    0.0277777779 * 100 = 2.77777779% <-- this is P[gray, thengray] or the probability of pulling out a gray pair on the first try and then again on the second try

    TO SUMMARIZE:
    P[gray] = 16.6666667% (the probability of pulling out a gray pair on the first try)
    P[gray, thengray] = 2.77777779% (the probability of pulling out a gray pair on the first try and then again on the second try)

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