Two separate draw bowls with distinct colored balls. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Two mechanisms can both be called a bonus ball
A bonus number drawn from a separate machine or pool can form an independent event under the stated model. A bonus ball drawn from the unused numbers in the main pool is conditioned on the main draw. These mechanisms should not share a formula merely because their descriptions contain the word “bonus.”
Multiply genuinely separate events
Suppose a toy main event has probability 1/10 and an independent separate bonus event has probability 1/3. The probability that both occur is 1/30, approximately 3.3333%. The separate-pool option in the Lottery Calculator uses this multiplication after calculating each pool's exact-match event.
See what changes for a leftover main-pool ball
In a five-number pool, draw two main numbers and then one bonus from the three remaining numbers. Conditional on exactly one main-number match with a fixed two-number ticket, one of the three remaining balls is the unmatched ticket number. Its conditional bonus probability is 1/3. That denominator comes from the remaining main pool, not from an independent pool selected without reference to the main outcome.
Read the actual rule structure before entering values
Selected-number counts, main-draw counts, bonus timing and the meaning of a prize category all matter. The current tool does not implement leftover-main-pool bonus rules, so leave its separate bonus pool disabled for that setting rather than forcing a superficially similar input. The hypergeometric guide explains the supported main event. For a general dependent product, use the Joint Probability Calculator with the correct conditional factor instead of assuming independence.
Check the model behind your result
Use the Lottery Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26