Answer:
An urn contains 3 red balls, 2 green balls and 1 yellow ball. Three balls are selected at random and without replacement from the urn. What is the probability that at least 1 color is not drawn?
The chance of not getting any color will be the chance of 1 minus getting a ball of each color:
P(red) = 3/6
P(green after red) = 2/5
P(yellow after green after red) = 1/4
0.5 x 0.4 x 0.25 = 0.05
Let's say we do a different sequence:
P(yellow) = 1/6
P(red after yellow) = 3/5
P(green after red after yellow) = 2/4
0.16666 x 0.6 x 0.5 = 0.05
As you can see, we get 1, 3, 2 as numerators and 4,5,6 as denominators too!
So, (trust me on this one) for every possible combination, the result probability will be 0.05!
How many combinations are there?
RGY
RYG
YGR
YRG
GRY
GYR
So 6 possible combinations. The 0.05 probability of each, times 6 is 0.3
And finally, the probability of not getting unique colors is the probability of all outcomes minus the ones we found out, in other words: 1 - 0.3 = 0.7
So the answer is 70%
©Fernando Cavalcanti Jeronymo
