Mathematical chance, random events, and probability models. Analysis of observed samples belongs in Statistics.
Test your knowledge with these top questions!
A game's expected prize is $3. What ticket price makes the expected net gain zero?
A mathematically fair price balances expected prizes and entry costs, though any one player can still win or lose.
On a fair European roulette wheel, what is the chance of zero on two consecutive independent spins?
Each spin must land on zero, so the two 1-in-37 chances multiply rather than add.
Three fair coins are tossed independently. What is the chance of at least one head?
Three tails is the only way to miss a head, so subtracting that outcome's chance from 1 gives the answer.
For three distinct lottery numbers, how many different draw orders are possible?
A fourth distinct number raises the count to 24 because that number can fit into four positions in each existing order.
What does a $5 expected payout guarantee for a single play?
A game can award only $2 or $8 and still have a $5 expected payout when both outcomes are equally likely.
In a random walk, what determines each step's direction?
A die or coin can supply the choices, so repeating the same rules can produce a different route each time.
How many independent random one-sticker packets guarantee all four equally likely sticker types?
Even a long run of identical stickers has a nonzero chance, so an average completion time is never a guarantee.
On a fair European roulette wheel, what is the chance of landing on one chosen number?
The layout groups numbers by color, parity, and range, but every individual number still has the same chance.
With a cyclic set of nontransitive dice, which strategy guarantees you can select the favored die?
The second chooser still sometimes loses because a favored matchup changes the odds without controlling each roll.
From a standard 52-card deck, what is the chance of randomly drawing a heart or an ace?
The ace of hearts belongs to both groups, so adding 13 hearts and four aces counts that card twice.