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 exactly 1 red?

Answer 1

Answer:

Assuming random distribution of marbles as well as random selection of marbles, the probability of getting 1R from among 5B, 6R and 2G = 6/13. Since the selected marble is replaced, the probability of getting a 2nd R = 6/13 as well. Thus the probability of getting 2R after 2 marble draws = (6/13)^2 = 36/139 = .2589928…~ 25.9%.

You could also consider the number of ways to select 2R from 6R with replacement = (6^2)/2 = 18. Then consider the ways of selecting any 2 marbles from 13 = (13^2)/2. Thus probability of getting 2R = 18/[(13^2)/2] = 36/139 = .2589928…~ 25.9%, as well.