Conditional probability thing

#1
I'm just trying to wrap my head around this...

Prob (A) = stop at 1st light = .4
Prob (B) = stop at 2nd light = .3
Prob (A and B) = .15

Whats the probability of stopping at just one light?
.4 x.7 + .6 x .3 = .46 but a Venn tells me it's .4

Probability of stopping at only first light?
.4 x .7 = .28 but a venn tells me it's .25

I know this has to do with the fact that they aren't independent events. I believe the correct answers are .46 and .25. Why use the venn in one and not the other?

Thanks!
 
#2
Interesting enough, for the first question, if I add (.15x.15) + (.15x.25) to the .4 from the venn, it turns my .4 to the correct .46... an explanation of that would be a bonus!
 
#5
Thanks for responding. I'm a tutor (stats aren't my specialty, but I dabble) and my student's book said .46 for stopping at only 1 of the 2 lights and .25 for stopping at only the first light.

Based on your input OBH, it sounds like that .46 is a mistake. A venn or the correct, non-independent events formula says its .4
 

obh

Well-Known Member
#6
Hi Yoyomccutch,

If I understand correctly the question I would go for the Ven.
Did they write in the question anything about independence?
You may send a question to the book author ...
 

obh

Well-Known Member
#8
They don't need to - the probabilities imply that the events aren't independent.
That what I proved before , but we didn't read the question ourself , from my experience most of the mistakes happened when you don't read the question correctly.
 

Dason

Ambassador to the humans
#9
I mean sure. But I find it highly unlikely that somebody would copy the probabilities incorrectly in such a way that some of the answers still worked out correctly.
 

obh

Well-Known Member
#10
I mean sure. But I find it highly unlikely that somebody would copy the probabilities incorrectly in such a way that some of the answers still worked out correctly.
Per my understanding, the correct answers are not in the book ...so they might mean independent events. anyway it doesn't matter