Thread: Probability theory

Conditions: Suppose that a coin is flipped and a die is rolled. Let E_1 denote the Event "the coin shows a tail," let E_2 denote the event "the die shows a 3" and let E_3 denote the event "the coin shows heads and the die shows an odd number."

Problem: Are E_1 and E_2 mutually exclusive?


I am pretty much lost here and really dont even know where to start.

Pwr

This was accidentally posted in the wrong forum. Sorry

Originally Posted by pwr_hngry

Conditions: Suppose that a coin is flipped and a die is rolled. Let E_1 denote the Event "the coin shows a tail," let E_2 denote the event "the die shows a 3" and let E_3 denote the event "the coin shows heads and the die shows an odd number."

Problem: Are E_1 and E_2 mutually exclusive?


I am pretty much lost here and really dont even know where to start.

Pwr

No draw a Venn diagram of the situation. Are the areas represented by
E1 and E2 disjoint? No they overlap whenever both the coin shows a tail
and the die a 3. Therefore they are not mutually exclusive.

RonL

Hello, pwr_hngry!

Suppose that a coin is flipped and a die is rolled.
Let E1 denote the event: "the coin shows a tail".
Let E2 denote the event: "the die shows a 3".

Problem: Are E1 and E2 mutually exclusive?

How about starting with the definition of "mutually exclusive".
. . You don't know it?

Two events are mutually exclusive if they cannot happen at the same time.


Flip a coin and roll a die.
Is it possible to get a "tail" on the coin and a "3" on the die?

Well?

Soroban,
By that definition of Mutually exclusive, it is definitely possible to roll a 3 on the die and have heads show on a coin. This would mean that tha E_1 and E_2 are NOT mutually exclusive.

Thanks for the Help Soroban and Captain Black.

Pwr.