Question

Define the independent events. Give an example for each of them:

a) Mutually exclusive

b) Independent

c) Dependent

- Can a pair of events be both mutually exclusive and independent?

Answer 1

Answer:-

Independent events:- In probability, two events are independent if the incidence of one event does not affect the probability of the other event.

Example:-

(a) Mutually exclusive event:-

Tossing a coin: Heads and Tails are Mutually Exclusive as occurrence of head implies does not occurrence of tail event.

(b) Independent event:-

Landing on heads after tossing a coin AND rolling a 5 on a single 6-sided die is an example of independent events.

(c) Dependent events:-

A bag contains 6 red, 5 blue and 4 yellow marbles. Two marbles are drawn, but the first marble drawn is not replaced then drawing the marbles is an example of dependent events.

Question:-Can a pair of events be both mutually exclusive and independent?

Answer:- If at least one of the events has zero probability, then the two events can be mutually exclusive and indepenent simultaneously. However, if both events have non-zero probability, then they cannot be mutually exclusive and independent simultaneously.