# Simple probability question

• Oct 5th 2010, 12:30 AM
Stroodle
Simple probability question
Kim goes to the sports centre each evening and either works out in the gym or has a swim. She never has a swim two evenings in a row. If she has a work-out in the gym one evening, then the next evening she is twice as likely to have a swim as she is to have a work-out in the gym. On a particular Monday evening, she works out in the gym.

What is the probability that she works out in the gym on both the Tuesday and Wednesday evenings of that week?

I can see that Pr(swim|swim)=0, and that Pr(gym|swim)=1. Just can't get my head around how to get Pr(gym|gym) and Pr(swim|gym).

Thanks for your help!
• Oct 5th 2010, 01:12 AM
downthesun01
Since,"if she has a work-out in the gym one evening, then the next evening she is twice as likely to have a swim as she is to have a work-out in the gym."

I would say that:

pr(gym|gym)=1/3

pr(swim|gym)=2/3

Since the sum of the two probabilities must equal 1 because it's stated that she does some sort of work out every evening.
Someone please correct me if I'm wrong.
• Oct 5th 2010, 01:19 AM
Stroodle
Ahh, of course. That's the same answer as in my text :)

Thanks heaps :)