Calculate exact-match probabilities for one unordered lottery ticket, with an optional separate independent bonus pool.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
P(exactly k matches)=C(r,k)C(N−r,r−k)/C(N,r). A separate independent bonus-pool event multiplies the main probability.
Assumptions and limits
Uniform draws without replacement, one unordered ticket, same count of selected and drawn numbers. Optional bonus pool is separate and independent; same-pool bonus balls, multiple tickets and actual prize schedules are not modeled.
Worked example
For a six-number ticket and six-number draw from 49, an exact six-match outcome has probability 1/C(49,6)=1/13,983,816. Leave the separate bonus pool at zero when it is not part of the model.
Worked reading and practical questions
- Count Exact Lottery Matches with a Hypergeometric Model
- A Separate Bonus Pool Is Not a Leftover Main-Pool Ball
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
Uniform draws without replacement, one unordered ticket, same count of selected and drawn numbers. Optional bonus pool is separate and independent; same-pool bonus balls, multiple tickets and actual prize schedules are not modeled.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.