Answer to Question #225975 in Statistics and Probability for Mustafa Zaidi

Question

Two 4-sided dice are tossed and the sum of the down sides noted. A 4-sided die doesn’t have an “up” face like a 6-sided die has, so the down side is used. Create a probability distribution table for this experiment. Type out your full solution.please need it NOW

Answer 1

$P\left(X=2\right)\:=P\left(both\:sides\:show\:1\right)\:=\frac{1}{16}\left(one\:outcome\:\left(1,1\right)\right)$

$P\left(X=3\right)\:=\frac{2}{16}=1/8\:\left(two\:outcomes\:\left(1,2\right),\left(2,1\right)\right)$

$P\left(X=4\right)\:=\frac{3}{16}\left(three\:outcomes\:\left(1,3\right),\left(2,2\right),\left(3,1\right)\right)$

$P\left(X=5\right)=\frac{4}{16}\:=\frac{1}{4}\:\left(four\:outcomes\:\left(1,4\right),\left(2,3\right),\left(3,2\right),\left(4,1\right)\right)$

$P\left(X=6\right)\:=\frac{3}{16}\left(three\:outcomes\:\left(2,4\right),\left(3,3\right),\left(4,2\right)\right)$

$P\left(X=7\right)=\frac{2}{16}\:=\frac{1}{8}\:\left(two\:outcomes\:\left(3,4\right),\left(4,3\right)\right)$

$P\left(X=8\right)=\frac{1}{16}\:\left(one\:such\:outcome\:\left(4,4\right)\right)$

Therefore, from the above result, the probability distribution table is presented as follows: