Probability is a number from 0 to 1 that measures how likely an event is. P = 0 means impossible (rolling a 7 on a standard die). P = 1 means certain (rolling any number from 1–6). P = 0.5 is a 50-50 chance (like a fair coin flip). For equally likely outcomes, count how many outcomes satisfy your event and divide by the total. The complement rule ($P(\text{not }A) = 1 - P(A)$) is often easier — instead of counting what you want, count what you don't want and subtract. The addition rule adds probabilities of two events but subtracts the overlap to avoid double-counting.
A box contains 5 defective and 45 good bolts. If one bolt is selected, find the probability that it is not defective.
$$P(\text{not defective})=1-\frac{5}{50}=0.90$$
Final answer: 0.90 or 90%.
Two Dice: Sum of 7 or 11
Two fair dice are rolled. Find the probability the sum is 7 or 11.
Total outcomes = 36. Ways to get sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6 ways. Ways to get sum 11: (5,6),(6,5) = 2 ways. Events are mutually exclusive (no overlap).
$$P=\frac{6+2}{36}=\frac{8}{36}=\frac{2}{9}$$
Final answer: $2/9 \approx 0.222$.
Mutually Exclusive Events
In a single roll of a die, find the probability of getting a 2 or a 5.
These events are mutually exclusive (both cannot happen at once), so $P(A \cap B) = 0$.
