**Independent Events**

Events
are considered

**independent events**if the occurrence of one has no bearing on the probability of the occurrence of the other. A good example to illustrate this is the tossing of a fair coin. A coin has no memory, meaning that even if a head comes up 10 times in a row, the probability that the next toss is a head is still ½. The probability that the next toss is a tail is also ½. The probability that the toss of a fair coin lands heads up or tails up on any single toss is always ½ no matter how many times the coin has been previously tossed.
If
two events

*A*and*B*are independent, then*P*(*A*∩*B*) =*P*(*A*) ∙*P*(*B*).
•

**Note that the rule for independent events can be extended for more than 2 events. If there are 3 independent events,***A, B*and*C*, then*P*(*A*∩*B ∩ C*) =*P*(*A*) ∙*P*(*B*) ∙*P*(*C*). Similar results are seen for 4 events, 5 events and so on.**Example:**Suppose a spinner has 12 regions numbered 1 – 12 each of which the spinner is equally likely to land on. What is the probability that the spinner will land on 2, 2, 10, 9 and any odd number in 5 consecutive spins?

*P*(2) = 1/12

*P*(10) = 1/12

*P*(9) = 1/12

*P*(odd) = ½

Therefore,
since these are independent events, the probability the spinner lands
on 2, 2, 10, 9 and any odd number in 5 consecutive spins is

(1/12)(1/12)(1/12)(1/12)(1/2)
= 1/41,472