Selected Answers to Problem Set #

3. See an example of my day of the week script here. It might be a bit complicated to follow, but notice the compensations for dates before March 1st and how the @MonthOffset array works. These might be of some use for you, especially with the problem for next week - day of the week for the web.

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4. Conversion between bases (a number with no base is base 10 by default). For reference (not for this class per se) a number prefixed with 0b indicates binary, 0 indicates octal, and 0x or $ indicates hexadecimal.
a) 76 = 64 + 8 + 4 = 2⁶ + 2³ + 2² = 1001100 base 2 (= 0b1001100 in computer terms)
b) 4321 base 8 (=04321 in computer terms)= 4*8³ + 3*8² + 2*8¹ + 1*8⁰ = 2048 + 192 + 16 + 1= 2257

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5. If the players win at these percentages, then they do no win at one minus these percentages. Simply take 0.7 * 0.8 * 0.75 to yield 0.42, or 42% of the time no one will win (or get a hit).

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6.

GC - Guilty of Crime
IC - Innocent of Crime
GT - Guilty on Test
IT - Innocent on Test

            P(GT|IC)P(IC)
P(IC|GT) = ---------------
                P(GT)

                    P(GT|IC)P(IC)
         = -------------------------------
            P(GT|IC)G(IC) + P(GT|GC)P(GC)

                  (0.02)(88)
         = -------------------------
            (0.02)(88) + (0.90)(12)

         = 1.76 / (1.76 + 10.80)

         = 0.14 = 14%

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