Question

There is a bag filled with 5 blue, 6 red and 2 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 green?

Answer 1

If there are 5 blue marbles, 6 red marbles, and 2 green marbles, then the probability of getting exactly 1 green marble is a 1.5 out of 10 chance. Here's why -

The chance of getting a red marble is a 63.4% chance.

The chance of getting a blue marble is a 43% chance.

Since there aren't many green marbles, the probability of getting ONE of two green marbles would be a 23.1% chance.

I'm using my own knowledge so I'm not completely sure if i'm correct or not.

I hope I helped. Have a good day.

Answer 2

The probability of getting exactly 1 green is 44/169

Total marbles = 5 blue + 6 red + 2 green

Total marbles = 13

The problem asks for exactly one green in 2 draws with replacement. Which means you could draw as follows:

Green, Not Green

Not Green, Green

The probability of drawing a green is 2/13, since we replace the marbles in the bag each time.

The probability of not drawing a green is (6 + 5)/13 = 11/13

And since each of the 2 draws are independent of each other, we multiply the probability of each draw:

Green, Not Green = 2/13 * 11/13 =22/169

Not Green, Green = 11/13 * 2/13 = 22/169

We add both probabilities since they both count under our scenario:

22/169 + 22/169 = 44/169

Therefore the probability of getting exactly  green is 44/169.

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