A jar consists of 21 sweets, 12 are green and 9 are blue. William picked 2 sweets at random. Find the probability that both sweets are blue.

What is (9/21)(8/20) ?

To find the probability that both sweets are blue, we need to determine the total number of possible outcomes and the number of favorable outcomes.

First, let's calculate the total number of possible outcomes. Since William picked 2 sweets from the jar, there are a total of C(21, 2) ways to choose 2 sweets from 21. The notation C(n, k) represents the number of combinations or ways to choose k items from a set of n items, without replacement.

The formula to calculate C(n, k) is:
C(n, k) = n! / (k! * (n - k)!)

In this case:
n = 21 (total number of sweets in the jar)
k = 2 (number of sweets William picked)

C(21, 2) = 21! / (2! * (21 - 2)!)
= 21! / (2! * 19!)
= (21 * 20 * 19!) / (2! * 19!)
= (21 * 20) / 2
= 420 / 2
= 210

Therefore, there are 210 possible outcomes when picking 2 sweets from the jar.

Next, let's calculate the number of favorable outcomes, i.e., the number of ways to choose 2 blue sweets from the 9 available blue sweets in the jar.
Since we are picking without replacement, the first sweet has a probability of 9/21 to be blue, and the second sweet has a probability of 8/20 to be blue.

Therefore, the number of favorable outcomes is:
9/21 * 8/20 = 72/420

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
P(both sweets are blue) = 72/420 ≈ 0.1714

Hence, the probability that both sweets William picked are blue is approximately 0.1714 or 17.14%.