Probability question

Question

A box contains 5 red marbles, 7 blue, 2 yellow, and 8 green marbles.   If 3 of the marbles are selected at random from the box, what is the probability that:

Round your answers to two decimal places.

i)   Two are red and one is blue.


 ii)   All three are different colors

Answer 1

The total number of marbles = 22

(i) Each time we pick a marble, the total remaining goes down by one. Although the order doesn't matter in this case, let's say we pick a red first (prob = 5/22), followed by another red (prob now = 4/21), then a blue (prob = 7/20). Overall probability = 5/22*4/21*7/20 = 140/9240,  = 1/66

 

(ii) The order again doesn't matter, but let's say we pick a red first (prob = 5/22), followed by a blue (prob = 7/21). It doesn't matter whether the next marble is yellow or blue (total = 8 + 2 = 10), so the probability of picking one of these is 10/20 = 1/2

 

So the overall probability = 5/22*7/21*1/2 = 35/924 = 5/132