# Conditional probability thing

#### Yoyomccutch

##### New Member
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!

#### Yoyomccutch

##### New Member
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!

#### Dason

Which answers are you claiming are correct? You seem to be inconsistent there.

#### obh

##### Well-Known Member
Hi Yoyomccutch,

Your calculation for 1. assumes independent events, if the events would be independent then P(A∩B)=p(A)*P(B)=0.4*0.3=0.12
But it is 0.15.

P(A diff B)=P(A)+p(B)-2*P(A∩B)

2. P(A but not B) = P(A) - (A∩B)

You may look for "dependent or independent" at https://www.statskingdom.com/probability-calculator.html

#### Yoyomccutch

##### New Member
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
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 ...

#### Dason

Did they write in the question anything about independence?
They don't need to - the probabilities imply that the events aren't independent.

#### obh

##### Well-Known Member
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.