ARML approaching

by b-flat, Jun 17, 2006, 3:21 PM

Yeah!! NC is leaving for ARML on Friday, and that is only 136,564 more seconds till we leave on Friday morning from the North Carolina School of Science and Mathematics.

I will be driving to Durham on Thursday night so I don't have to get up at 5 to leave.

Random problem (made up off the top of my head):

What is the probability of winning ARML if:
The probability of you getting the first question correct is $\frac78$
$2\Rightarrow\frac23$
$3\Rightarrow\frac56$
$4\Rightarrow\frac23$
$5\Rightarrow\frac12$
The probability of getting 6 is $\frac13$, but the probability of gettin both 5 and 6 is $\frac18$
$7\Rightarrow\frac12$
The probability of getting 8 is $\frac18$, but the probability of getting both 7 and 8 is $\frac1{20}$.

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It would depend on what the winning score would be, but assuming that it is $8$:

$P=\frac{7}{8}\cdot\frac{2}{3}\cdot\frac{5}{6}\cdot\frac{2}{3}\cdot\frac{1}{8}\cdot\frac{1}{20}=\boxed{\frac{7}{3456}}$

by Xantos C. Guin, Jun 17, 2006, 3:22 PM

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No, actually, I forgot to add that you only need 7 to win.

by b-flat, Jun 17, 2006, 3:22 PM

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