Sidney has 4 hats and 2 scarves in a drawer. All the hats are the same size, shape, and material. Both scarves are the same size, shape, and material. The table below shows the colors of Sydney's hats and scarves. Sidney will pick one hat and one scarf from the drawer without looking. What is the probability that Sidney will be a blue hat and a white scarf? Colors of Sidney's Hats and Scarves Hats Scarves 1 blue 1 green 1 red 1 white 1 yellow 1 purple O 1/8 O 1/6 1/4 O 1/2

Step-by-step explanation:

Given

Scarves: 1 green; 1 white

Hats: 1 blue; 1 red; 1 yellow; 1 purple

Required

Determine the probability of 1 blue hat and 1 white scarf

First, we need to determine the probability of blue hat

Hence;

Next, we determine probability of white scarf

Calculating the required probability;

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1