# Thread: Simple probability question

1. ## 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!

2. 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.

3. Ahh, of course. That's the same answer as in my text

Thanks heaps