5 + 2 Dual Chamber Number Picker (50/12): How to use this preset
What the selection means
Two separate pools produce five main numbers from 1–50 and two secondary numbers from 1–12. Keep the two parts of the result separate: a main 7 and a secondary 7 refer to different pools. Within each pool, numbers do not repeat in the same set.
Using the controls
Choose the number of sets and a tumble time, then press Pick Numbers. Read the main and secondary results separately. Switching between selection order and sorted order changes the display, not which balls were picked. Each new set refills both chambers.
An activity to try
Label 50 activity cards and 12 constraint cards. For example, the activity cards can be drawing subjects and the constraints can be “use two colours” or “draw with straight lines”. Pick five subjects and two constraints, then apply both constraints to the activity. This uses all seven selections without treating them as one numbered list.
Create your own version with PhysPicks
Set the number range and pick count for each chamber to build a two-part game, such as prompts and instructions.
Create a dual-chamber gameWhat are the probabilities?
These calculations assume uniform selection without replacement within each pool and independent chambers. They describe a mathematical model, not measured or certified probabilities for the PhysPicks physics simulation.
| Event defined before the selection | Theoretical probability |
|---|---|
| One specified main number is the first ball out | 1/50 ≈ 2% |
| One specified main number appears anywhere in the completed set | 5/50 ≈ 10% |
| Exactly one of your 5 preselected main numbers matches (secondary pool ignored) | 744,975/2,118,760 ≈ 35.16% |
| One specified secondary number appears in the secondary selection | 2/12 ≈ 16.67% |
| One specified complete combination, ignoring order | 1/139,838,160 |
C(50,5) × C(12,2) = 139,838,160
For k picks from n numbers, a specified number is included with probability k/n. There are C(n,k) = n! / (k!(n−k)!) unordered sets. With two independent pools, multiply their combination counts. “One specified number appears” is different from “exactly one of my chosen numbers matches”. A previous result does not make a number due next time.
P(X = 1) = C(5,1) × C(45,4) / C(50,5)