Help with this!

Question

Help with this!

anonymous · Answer

with what??

anonymous · Answer

attachment

anonymous · Answer

oh i see

anonymous · Answer

sooo??

anonymous · Answer

@hartnn

anonymous · Answer

dependent events are not necessarily mutually exclusive

anonymous · Answer

if iam not wrong , mutually exclusive events are independent right?

anonymous · Answer

so forget about II  it is wrong
no no, mutually exclusive and independent are two separate conceps
in fact, if you know the events are mutually exclusive they are DEPENDENT because if you know one occurs you know the other does not occur

anonymous · Answer

so III is correct, mutually exclusive events are dependent

anonymous · Answer

i am confused!

anonymous · Answer

ok lets give a simple example

anonymous · Answer

sure!

anonymous · Answer

it is not possible for you to roll a die and get both a total of 7  and a total of 8 right?

anonymous · Answer

those events are MUTUALLY EXCLUSIVE because their intersection is empty

anonymous · Answer

i mean roll dice, not a single die that was my mistake
but it is not possible to roll two dice and get 7 and 8 at the same time, 
you can get a 7 or
you can get an 8 but
you cannot get both

anonymous · Answer

now if i say A is the event you roll a 7, and B is the event you roll an 8, then 
$$P(A|B)=0$$ because if you know you rolled an 8 you know you did not roll a 7

anonymous · Answer

why? if i roll two dice i can get 7 on one and 8 on the other?

anonymous · Answer

since $P(A|B)=0$ but $P(A)=\frac{1}{6}$ we know these events are DEPENDENT

anonymous · Answer

oh no sorry i got it

anonymous · Answer

you meant a total of 7 and total of 8 right?

anonymous · Answer

and what does this mean P(A|B)?

anonymous · Answer

right

anonymous · Answer

where were you gone???

anonymous · Answer

this means that 
$$P(A|B)=0$$ because if you know you have rolled an 8, you know you cannot have rolled a 7

anonymous · Answer

and therefore A and B are DEPENDENT

anonymous · Answer

so III is correct

anonymous · Answer

now how about I ?

anonymous · Answer

the line between alpha bet A nd B indicates what in this P(A|B)?

anonymous · Answer

refresh your browser
you should be able to see P(A|B)

anonymous · Answer

as for I, if A and B are independent, that means
$$P(A\cap B)=P(A)\times P(B)$$

anonymous · Answer

either way it is a line just like it is in question!

anonymous · Answer

yes

anonymous · Answer

if $P(A)>0$ and $P(B)>0$ then 
$$P(A)P(B)>0$$

anonymous · Answer

so A and B cannot be mutually exclusive

anonymous · Answer

so the answer is C?