Contrasting independent and mutually exclusive events
These are two very important concepts and there are two rules associated with them.You should have seen this notation: P(A) stands for the probability that event A happens.
| Independent | Mutually exclusive | |
| Meaning | events that have no connection with each other | events that cannot happen together |
| Example | Whether you have cereal or bacon for breakfast, and whether it rains the same morning in Marseille. | Rolling a dice and it comes up 3, the same roll comes up 4 |
| Probability rule | Multiplicaton rule: If A and B are independent, then P(A AND B) = P(A) x P(B) |
Addition rule: If A and B are mutually exclusive: P(A OR B) = Prob(A) + P(B) |
| Worked example: | If I roll a dice and toss a coin, what is the probability of getting a 3 and a head? | If I roll a dice, what is the probability of getting a 1 or a 3? |
| Answer: | P(3) = ⅙, P(Head) = ½ So P(3 and H) = ⅙ x ½ = 1/12 |
P(1)=⅙, P(3)=⅙, so P(1 or 3)=&frac26; = ⅓ |