Suppose there are 2 blue, 2 yellow and 2 red in a bucket. If you pick two balls, at random, without replacement, what is the probability that the two balls will be of the same color?

llm

Answered on Fri Jun 24 2022

We have,

Number of blue balls = 2

Number of yellow balls = 2

Number of red balls = 2

Total balls = 2 + 2 + 2 = 6

Now, probability = Favorable outcome/Total outcome

So, probability of picking blue ball = 2/6

= 1/ 3

Now, without replacement, Remaining balls are 5

And Number of blue ball is 1

So, probability of picking blue ball = 1/5

Then, probability of picking blue balls back to back without replacement = 1/ 3 × 1/5

= 1/15

Similarly, probability of picking red and yellow balls without replacement is also 1/15