You draw a marble, replace it, and then draw another marble. What is the probability of choosing two yellow marbles?

Answer 1

Let's say there are 100 marbles and 20 are yellow

then chance of a yellow on one draw is 20/100 = 20% = .2

with replacement, odds of yellow on the 2nd draw is the same = .2

odds of 2 yellows (2/10)^2 = 4/100 = .2 x .2 = .04 = 4%

in general, with y/m = the ratio of yellow to total marbles, y= number of yellow, m=number of all marbles

odds of two yellow on two draws, without replacement

= (y/m)^2 = y^2/m^2