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# A point (x,y) with integer coordinates is randomly selected such that and . What is the probability that ? Express your answer as

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A point  (x,y) with integer coordinates is randomly selected such that \(\$0 \le x \le 8\$\) and \(\$0 \le y \le 4\$\). What is the probability that \(\$x + y \le 4\$\)? Express your answer as a common fraction.

Nov 12, 2017

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x =  { 0, 1 , 2, 3 , 4, 5, 6, 7 ,8 }

y =  { 0, 1, 2, 3, 4 }

There are 45 possible sums  [ many repeated ]

The ones  ≤ 4 are

x

0        can be paired with 5 y terms

1        can be paired with 4 y terms

2        can ve paires with  3 y terms

3        can be paired with  2 y terms

4        can be paired with  1  y term

So...the probability  that  x + y  ≤  4  is

[ 1 + 2 + 3 + 4 + 5] / 45  =  15 / 45  =     1 / 3

Nov 12, 2017