Please help. Very hard probability question with unusual wording

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SUMMARY

The discussion revolves around a probability problem involving transport modes, specifically the likelihood of catching a bus or driving a car based on previous choices. The probabilities are defined as 0.7 for catching the bus after catching it the previous day and 0.25 for catching the bus after driving. The user seeks assistance in applying Bayes' Theorem to calculate the probability of various scenarios, particularly the probability of catching the bus on Wednesday given that the user drove on Monday.

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Homework Statement



Suppose that each day I either catch the bus to work or drive my car to work. Suppose that the
probability I catch the bus on any particular day only depends on the mode of transport I used on the
previous day, and is 0.7 if I caught the bus on the previous day and 0.25 if I drove my car to work.
(a) What is the probability I drive my car to work tomorrow given that I caught the bus today?
(b) What is the probability I catch the bus to work?
(c) What is the probability I caught the bus yesterday given that I caught the bus today?
(d) What is the probability I catch the bus on Wednesday given that I drove by car to work on
Monday?
2

Homework Equations


none


The Attempt at a Solution


How do you do this?

Especially D. i think you use bayed theoram.

Just don't know how to do D !
 
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