The probabilities change depending on where you are, how old you are and what you are doing, Yeti.
You and others might enjoy a short read about cougar from the B.C. government.
Safety Guide to Cougars
http://www.env.gov.bc.ca/wld/documents/cougsf.htmand about bears from
http://www.bearsmart.com/index.htmlNothing can replace good sense and proper safety measures. People whose activities may possibly put them in a situation where they may encounter a bear or other wild animal should educate themselves and be aware of the potential for an attack. Carrying animal repellent does not warrant careless or disrespectful behaviour. It does, however, provide an alternative to physical violence or lethal means when a potentially life-threatening situation arises.
and
Are you Bear Wise? eBook
http://www.mnr.gov.on.ca/en/Business/Bearwise/Publication/196982.html