Lottery Odds Explained

Complete guide to lottery odds and probability. Learn mathematical formulas, verified calculations, and how lottery odds work from official sources.

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Verified Lottery Odds Calculations

Powerball Calculation #1

Powerball Jackpot Odds

Odds:

1 in 292,201,338

Formula:

C(69,5) × C(26,1) = 292,201,338

Mathematical Explanation:

Choose 5 from 69 main numbers and 1 from 26 Powerball numbers

Mega Millions Calculation #2

Mega Millions Jackpot Odds

Odds:

1 in 302,575,350

Formula:

C(70,5) × C(25,1) = 302,575,350

Mathematical Explanation:

Choose 5 from 70 main numbers and 1 from 25 Mega Ball numbers

EuroMillions Calculation #3

EuroMillions Jackpot Odds

Odds:

1 in 139,838,160

Formula:

C(50,5) × C(12,2) = 139,838,160

Mathematical Explanation:

Choose 5 from 50 main numbers and 2 from 12 Lucky Star numbers

Verified Probability Concepts

Combination Formula

Formula:

C(n,r) = n! / (r! × (n-r)!)

Example:

C(69,5) = 69! / (5! × 64!) = 11,238,513

Explanation:

Calculates the number of ways to choose r items from n items without regard to order

Independent Events

Formula:

P(A and B) = P(A) × P(B)

Example:

Drawing main numbers and Powerball are independent events

Explanation:

The probability of two independent events both occurring

Mutually Exclusive Events

Formula:

P(A or B) = P(A) + P(B)

Example:

Winning different prize levels are mutually exclusive

Explanation:

The probability of either of two mutually exclusive events occurring

Verified Odds Comparisons

Event	Odds	Probability	Comparison	Source
Winning Powerball Jackpot	1 in 292,201,338	0.000000342%	More likely to be struck by lightning (1 in 1,222,000)	National Weather Service & MUSL
Winning Mega Millions Jackpot	1 in 302,575,350	0.000000331%	More likely to be killed by a vending machine (1 in 112,000,000)	Consumer Product Safety Commission & MUSL
Being struck by lightning	1 in 1,222,000	0.000082%	239 times more likely than winning Powerball	National Weather Service
Being killed by a shark	1 in 3,748,067	0.000027%	78 times more likely than winning Powerball	International Shark Attack File

Verified Prize Level Odds

Game	Match	Prize	Odds	Source
Powerball	5 + Powerball	Jackpot	1 in 292,201,338	MUSL Official Rules
Powerball	5 numbers	$1,000,000	1 in 11,688,053	MUSL Official Rules
Powerball	4 + Powerball	$50,000	1 in 913,129	MUSL Official Rules
Mega Millions	5 + Mega Ball	Jackpot	1 in 302,575,350	MUSL Official Rules
Mega Millions	5 numbers	$1,000,000	1 in 12,607,306	MUSL Official Rules
Mega Millions	4 + Mega Ball	$10,000	1 in 931,001	MUSL Official Rules