I've just been looking through my firewall log. In the 8 hours since I switched my computer off I have had 80 attempts by crooks attempting to breach my firewall plus 6 determined attacks. That works out that if I did not have my firewall in place, it would take between 5 and 6 minutes before my computer became infected.
A few years ago, some IT people deliberately tested a computer without a firewall to see how long it took to become infected. 8 seconds.