Difference between revisions of "2023 AMC 8 Problems/Problem 23"
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There are 9 squares and 4 possible designs for each square, giving <math>4^9</math> total outcomes. Thus, our desired probability is <math>\dfrac{4^6}{4^9} = \dfrac{1}{4^3} = \boxed{\text{(C)} \hspace{0.1 in} \dfrac{1}{64}}</math> . | There are 9 squares and 4 possible designs for each square, giving <math>4^9</math> total outcomes. Thus, our desired probability is <math>\dfrac{4^6}{4^9} = \dfrac{1}{4^3} = \boxed{\text{(C)} \hspace{0.1 in} \dfrac{1}{64}}</math> . | ||
-apex304, SohumUttamchandani, wuwang2002, TaeKim. Cxrupptedpat | -apex304, SohumUttamchandani, wuwang2002, TaeKim. Cxrupptedpat | ||
+ | |||
+ | ==Animated Video Solution== | ||
+ | https://youtu.be/f4ffQEG0yUw | ||
+ | |||
+ | ~Star League (https://starleague.us) |
Revision as of 19:22, 24 January 2023
Probability is total favorable outcomes over total outcomes, so we can find these separately to determine the answer.
There are ways to choose the big diamond location from our
square grid. From our given problem there are
different arrangements of triangles for every square. This implies that from having
diamond we are going to have
distinct patterns outside of the diamond. This gives a total of
favorable cases.
There are 9 squares and 4 possible designs for each square, giving total outcomes. Thus, our desired probability is
.
-apex304, SohumUttamchandani, wuwang2002, TaeKim. Cxrupptedpat
Animated Video Solution
~Star League (https://starleague.us)