Probability of getting exactly 2 purple when picking 5 from 20 objects (8 purple, 12 grey)
39.7317%
6160 favorable out of 15504 total outcomes
Object Pool
Combinations Breakdown
Choose 2 purple from 8
C(8, 2) = 28
Choose 3 grey from 12
C(12, 3) = 220
... and 205 more
Favorable outcomes = 28 × 220 =6160
Total Outcome Space
With 20 objects and picking 5, there are 15504 possible outcomes. (Too many to visualize individually)
Formula
Step 1: Ways to choose purple
Step 2: Ways to choose grey
Step 3: Favorable outcomes
Step 4: Total outcomes
Step 5: Probability
Probability is at its heart a ratio of desired outcomes to all possible outcomes. This tool helps you visualise just that. Say you had a pool of objects — some grey, some purple — and you were to randomly draw 5 objects from it wanting exactly 2 purple, you should be able to see above all the scenarios in which your selections could play out.
Probability is best understood through the lens of combinatorics — a branch of maths that has to do with permutations and combinations — because this way you account for every possible scenario (both desired and total).
Personally, I understood this first through the famous handshake problem, which asks: how many handshakes are possible among a group of n persons where no two persons shake hands with each other more than once? This is the basis for "selections". That's part of the reason why I've visualised selecting the purple objects by arranging them in a circle. It's akin to asking - how many connections exist between any n points in the circle.