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Count all equally likely outcomes and count the outcomes that satisfy the condition. The probability is the number of favorable outcomes divided by the total number of outcomes: \(P(E)=\frac{\text{favorable outcomes}}{\text{total outcomes}}\). For example, rolling two dice gives \(6\times6=36\) equally likely pairs. The pairs summing to 7 are \((1,6),(2,5),(3,4),(4,3),(5,2),(6,1)\), six favorable outcomes, so \(P(\text{sum }7)=\frac{6}{36}=\frac16\). For "at least one" events, it is often easier to count the complement: outcomes where the event does not happen, then subtract from the total.
Curated
12| # | Title | Difficulty | Source | Tags | |
|---|---|---|---|---|---|
| 179 | Lucky seven | Easy | Lemma | ||
| 180 | The Chevalier's wager | Easy | Classical | ||
| 421 | A heart or a king | Easy | Lemma | ||
| 422 | Exactly two heads | Easy | Lemma | ||
| 423 | Ten or more | Easy | Lemma | ||
| 424 | Two aces in a row | Easy | Lemma | ||
| 425 | On the committee | Easy | Lemma | ||
| 426 | A PIN with no repeats | Easy | Lemma | ||
| 427 | Who comes first? | Easy | Lemma | ||
| 1816 | Contradicting the same fact | Easy | Hall & Knight | ||
| 1895 | Coins Distributed in Purses Part 1 | Easy | Hall & Knight | ||
| 428 | A flush | Medium | Lemma |
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