Probability: mutually exclusive vs. disjoint events

[VonWeber]

Homework Statement

Are all disjoint events also mutually exclusive? And if events are independent does this also mean that they cannot be disjoint?

Homework Equations

no relevant equations

The Attempt at a Solution

In probability disjoint events are events that have no intersection. If the events have no intersection I would think that they would have to be mutually exclusive and could not be independent either because there is no way for them to both occur at the same time.

 

[jing]

mutually exclusive and disjoint are the same as you say the intersection is the empty set.

Two events are independent if and only if P(A intersect B)=P(A).P(B) so again you are right mutually exclusive events cannot be independent and vice versa.

Yo cannot throw a dice and get an odd number and an even number at the same time - mutually exclusive

You can throw two dice and the probability of getting two sixes is 1/36 which is the probability of getting a six on one x probability of getting a six on the other - two dice are independent of each other

P(6 & 6) =P(6).P(6)



Throwing one die
Probability of throwing an odd prime number {3,5} two out of six or 1/3

P(odd number and a prime number) =1/3
p(odd number) =1/2
p(prime number) =1/2

P(odd number and a prime number) not= p(odd number).P(prime number) so not independent events

A number being prime is independent on it being odd

Hope this helps