What is the probability of drawing two blue balls (both blue) from the bag?

• A. 2/21
• B. 3/21
• C. 1/21
• D. 4/21

Answer: (C)

When you draw two balls without replacement, you can think of it in two ways. One clear way is to use combinations: there are 7 balls in total with 2 blue. The number of ways to pick any two balls is C(7,2) = 21, and the only favorable outcome is picking both blues, which is C(2,2) = 1 way. So the probability is 1/21.

A quick check using sequential probability also works: the chance the first ball is blue is 2/7, and if that happens, the chance the second is blue is 1/6. Multiply them: (2/7) × (1/6) = 2/42 = 1/21. Both perspectives give the same result.