Answer to Question #170051 in Statistics and Probability for Shaina

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

Total marbles = 13

The problem asks for exactly one blue 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.

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

P(Green, Not Green) $= \frac{2}{13} \times \frac{11}{13} = \frac{22}{169}$

P(Not Green, Green) $= \frac{11}{13} \times \frac{2}{13} = \frac{22}{169}$

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

P(exactly 1 green) $= \frac{22}{169} + \frac{22}{169}$

$= \frac{44}{169} \\ = 0.2603$