user
A box contains 12 red balls, 18 blue balls, and 6 green balls. If you randomly pick two balls from the box without replacement, what is the probability that both balls are blue?
assistant
To find the probability, we need to calculate the number of favorable outcomes (picking two blue balls) divided by the total possible outcomes (picking any two balls). Here's how:

1. There are a total of 36 balls in the box (12 red + 18 blue + 6 green).
2. The total number of ways to pick two balls from the box is given by the combination formula: C(n, k) = n! / [k!(n-k)!], where n is the total number of items and k is the number of items being chosen. In our case, n = 36 and k = 2.

Total Outcomes = C(36, 2) = 36! / [2!(36-2)!] = (36*35) / (2*1) = 630

3. Now, we need to find the number of favorable outcomes, which is picking two blue balls from the 18 available. Using the same combination formula with n = 18 and k = 2:

Favorable Outcomes = C(18, 2) = 18! / [2!(18-2)!] = (18*17) / (2*1) = 153

4. Finally, we can calculate the probability by dividing the number of favorable outcomes by the total possible outcomes:

Probability = Favorable Outcomes / Total Outcomes = 153 / 630

So, the probability that both balls are blue is 153/630 or approximately 0.243.