conditional probability question

Hi;
Jean always goes to work by bus or taxi,If one day she goes to work by bus the probability
that she goes by taxi the next day is 0.4,If one day she goes by taxi the probability she goes by bus the next day is 0.7

Given that on monday she goes by bus,Whats the probabilty she goes by taxi on wednesday.

What I have
On monday she has an equal chance of taxi or bus probabilty=0.5each
On tuesday she has a 0.4 probability by taxi and 0.6 by bus but we don,t know which she took.

If she took the bus she has a 0.4 probability by taxi and 0.6 probability by bus
If she took a taxi she has a 0.7 probability by bus and a 0.3 probabity by taxi.



Stuck here
Do I add the probabilities of the wednesday ie 0.4(taxi) + 0.3(taxi) and just divide them by 2?

You are given that she took the bus on Monday ("Given that on monday she goes by bus..."). So your statement "On monday she has an equal chance of taxi or bus probabilty=0.5each" is wrong. With 100% probability, she took the bus on Monday.

Of course I missed that bit
Heres A badly drawn tree diagram of what I think is correct


Attachment 27279

Here's a hint - look at the formula for Total Probability: P[A] = P[A|B]*P[B] + P[A|C]*P[C], (given events A,B,C)
You could write: P[Wed=Taxi] = P[Wed=Taxi | Tue=Taxi]*P[Tue=Taxi] + P[Wed=Taxi | Tue=Bus]*P[Tue=Bus]

Now you need to figure out how to get P[Tue=Taxi] and P[Tue=Bus]. Again, P[Mon=Bus] = 100%, and P[Mon=Taxi] = 0%.

Oops- I just saw your drawing.. taking a look.

OK, I modified the drawing a little. Does this make sense? Attachment 27280

Yes thanks.