What is the difference between independent and mutually exclusive events?
SHORT ANSWER
Independent events do not affect each other: P(A and B) = P(A) x P(B). Mutually exclusive events cannot happen together: P(A and B) = 0. Two events with non-zero probability cannot be both.
Explain it simply
- Independent: whether it rains in Mumbai today has no bearing on the result of a coin flip in Delhi.
- Mutually exclusive: on a single coin flip, heads and tails cannot both happen.
Mutually exclusive events are actually strongly dependent. If one occurs, you know for certain the other did not.
Example
Roll one die.
- A = even number, B = number greater than 4. P(A) = 3/6, P(B) = 2/6, P(A and B) = P(6) = 1/6.
- Check independence: P(A) x P(B) = 1/2 x 1/3 = 1/6, which equals P(A and B). So A and B are independent, even though they overlap.
- C = number 1, D = number 2: P(C and D) = 0. They are mutually exclusive, but P(C) x P(D) = 1/36, not 0, so they are not independent.
python
from fractions import Fraction as F
print(F(1, 2) * F(1, 3)) # 1/6What to say in the interview
"Independence means knowing one event gives no information about the other, so probabilities multiply. Mutually exclusive means the events cannot share an outcome, so probabilities add: P(A or B) = P(A) + P(B). If events are mutually exclusive and both possible, they are dependent, not independent."
Common mistakes
- Using the multiplication rule for events that are not independent, such as drawing cards without replacement.