Counting & chance

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.