Answer to Question #304890 in Statistics and Probability for ced

Question

Wood paneling can be ordered in thickness of 1/16,1/8,1/4, or3/8inch. The random variable

X is the total thickness of paneling in two orders. List the elements in the sample

space.

Answer 1

Since all wood paneling has different thickness, then there are ${4 \choose 2}+4=10$ different combinations of 2 wood paneling. Let's find total thickness for every of them

${\frac 1 {16}}+{\frac 1 {16}}={\frac 1 8}$

${\frac 1 {16}}+{\frac 1 {8}}={\frac 3 {16}}$

${\frac 1 {16}}+{\frac 1 4}={\frac 5 {16}}$

${\frac 1 {16}}+{\frac 3 8}={\frac 7 {16}}$

${\frac 1 8}+{\frac 1 8}={\frac 1 4}$

${\frac 1 8}+{\frac 1 4}={\frac 3 8}$

${\frac 1 8}+{\frac 3 8}={\frac 1 2}$

${\frac 1 4}+{\frac 1 4}={\frac 1 2}$

${\frac 1 4}+{\frac 3 8}={\frac 5 8}$

${\frac 3 8}+{\frac 3 8}={\frac 3 4}$

So, X = {${\frac 1 8},{\frac 3 {16}},{\frac 5 {16}},{\frac 7 {16}},{\frac 1 4},{\frac 3 8},{\frac 1 2},{\frac 5 8},{\frac 3 4}$}. X measures in inches