Sixty percent of the marbles in a bag are blue. One marble is chosen and replaced. A second marble is chosen and replaced. Then a third marble is chosen. What is the probability that a blue marble will not be chosen?

0.064. same as 8/125

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the total outcome.

Given that Sixty percent of the marbles in a bag are blue

The probability of picking a blue marble

p(b) = 60% = 3/5

The probability of not picking a blue marble

np(b) = 1 - 60%

= 1 - 3/5

= 2/5

Hence where 3 marbles are picked and replaced, the probability of not picking a blue marble

= 2/5 * 2/5 * 2/5

= 8/125

= 0.064

{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