Hannah has a bag containing 2 Red, 4 purple, 4 Blue and 2 Green marbles that all are the same size and shape. What is the
probability of randomly choosing a Red marble replacing it, and
then randomly choosing a Blue marble?

1/18

Step-by-step explanation:

there are 12 marbles in the bag

P(choose red) = 2/12 = 1/6

P(choose blue after replacement) = 4/12 = 1/3

P(choose red, then blue with replacement) = (1/6)(1/3) = 1/18

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)