In a bag of 25 coloured balls, 7 are orange, 6 are yellow and the rest are green. Laura picks out a ball and records its colour but doesn't return it to the bag, she then repeats this twice more. What is the probability of Laura getting 3 yellow balls?

Answer: 1/115

The easiest way to solve this problem is to draw part of a tree diagram to see the probabilites of each colour being picked each time Laura pulls a ball out of the bag (a full diagram isn't needed as only the probabilites on the branches that will be picked need to be included). The initial fractions are Orange (O) 7/25, Yellow (Y) 6/25 and Green (G) 12/25, for the second branch the denominator decreases by one as the first ball isn't replaced so becomes 24, the probabilites then become, O 7/24, Y 5/24 and G 1/2 (12/24). For the third branch the same happens again, the denominator becomes 23 and only the numerator for Y changes, O 7/23, Y 4/23, G 12/23. Then to calculate the probability of three yellow balls in a row multiply using your calculator the three probabilites of pulling a yellow ball out; P(YYY) = 6/25 x 5/24 x 4/23 = 1/115