A bag contains 4 green marbles, 6 red marbles, and 2 white marbles. Three marbles are drawn at random with replacement. With replacement means that after a marble is drawn, it is replaced before the next one is drawn. What is the probability of not green, not red, not white?

p(~g) = 8/12 = 2/3

p(~r) = 6/12 = 1/2
p(~w) = 10/12 = 5/6

p(~g,~r,~w) = 2/3 * 1/2 * 5/6 = 5/18

Not green = (6+2)/12

Not red = (4+2)/12

Not white = (4+6)/12

The probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

Oh, you want to avoid all the colors, huh? Well, let's calculate that probability and try not to be too colorful with our answer!

There are a total of 4 + 6 + 2 = 12 marbles in the bag. And for each draw, we have a 1/3 chance of not picking any specific color. So, the probability of not green, not red, and not white for one draw is 1/3 + 1/3 + 1/3 = 1.

Since we're drawing with replacement, each draw is independent of the others. So, the probability of not getting green, not red, and not white for all three draws is (1/3) * (1/3) * (1/3) = 1/27.

So, the probability of avoiding all the colors and drawing marbles that are not green, red, or white is 1/27.

To calculate the probability of not drawing a green, red, or white marble, we need to find the probability of drawing a non-green, non-red, and non-white marble in each of the three draws.

The number of marbles in the bag is 4 + 6 + 2 = 12.

The probability of not drawing a green marble in one draw is (12 - 4) / 12 = 8 / 12 = 2 / 3.

Similarly, the probability of not drawing a red marble in one draw is (12 - 6) / 12 = 6 / 12 = 1 / 2.

And the probability of not drawing a white marble in one draw is (12 - 2) / 12 = 10 / 12 = 5 / 6.

Since we are drawing with replacement, the probability of not drawing a green, red, or white marble in each of the three draws is independent events. So, we can calculate the overall probability by multiplying the probabilities of each individual draw:

P(not green, not red, not white) = P(not green in the first draw) * P(not red in the second draw) * P(not white in the third draw)

= (2/3) * (1/2) * (5/6)

Simplifying, we get:

= 5/18

Therefore, the probability of not drawing a green, red, or white marble is 5/18.

To find the probability of not drawing a green, red, or white marble, we need to find the probability of drawing a marble that is not green, not red, and not white in each of the three draws.

The total number of marbles in the bag is 4 green + 6 red + 2 white = 12 marbles.

The probability of drawing a marble that is not green in each draw is given by:

P(not green) = 1 - P(green) = 1 - (number of green marbles / total number of marbles)
P(not green) = 1 - 4 / 12 = 1 - 1/3 = 2/3

Similarly, the probability of drawing a marble that is not red in each draw is given by:

P(not red) = 1 - P(red) = 1 - (number of red marbles / total number of marbles)
P(not red) = 1 - 6 / 12 = 1 - 1/2 = 1/2

Lastly, the probability of drawing a marble that is not white in each draw is given by:

P(not white) = 1 - P(white) = 1 - (number of white marbles / total number of marbles)
P(not white) = 1 - 2 / 12 = 1 - 1/6 = 5/6

Since the three draws are independent events and we are drawing with replacement, we can multiply the probabilities to find the overall probability of not green, not red, and not white in all three draws:

P(not green, not red, not white) = P(not green) * P(not red) * P(not white)
P(not green, not red, not white) = (2/3) * (1/2) * (5/6)
P(not green, not red, not white) = 1/3

Therefore, the probability of not green, not red, not white is 1/3.