Method

To calculate the probability that multiple independent events won't occur, use the complement rule:

The complement rule states that the probability of an event not occurring (¬A) equals 1 minus the probability of it occurring (P(A)).

For multiple independent events, multiply the individual probabilities and subtract from 1.

The formula is:

$P(¬A and ¬B and ¬C and ...) = 1 - P(A) * P(B) * P(C) * ...$

Follow these steps:

1. Find the probability of each event occurring
2. Multiply these probabilities together (only for independent events)
3. Subtract from 1 to get the probability that none occur

Example

Let's calculate the probability of failing all three independent exams:

P(A) = 0.8 (passing exam A) P(B) = 0.7 (passing exam B) P(C) = 0.9 (passing exam C)

Calculation:

P(failing all) = 1 - P(passing all) = 1 - (0.8 × 0.7 × 0.9) = 1 - 0.504 = 0.496

Therefore, there's a 49.6% chance of failing all three exams.

Note: This method only works when the events are truly independent of each other.