This question (“will I get infected if people in my household are sick?”) was asked in the recent Reddit AMA with experts. Keep in mind I didn't verify the original sources.
“It is possible to stay uninfected! Yesterday in a press briefing, Dr. Nancy Messonnier at the CDC said that the secondary attack rate among family members of confirmed COVID-19 cases in the U.S. is 10.5% so far. So that means that about 1 in 10 family members who have been exposed by a relative have gotten sick.”
Here’s the posting and some more comments about this issue: https://www.reddit.com/r/Coronavirus/comments/fdf5fq/we_are_a_team_of_medical_experts_following/
Thinking about it with a toy model:
Assume you on average contact 25 people a day when you go out, and each of your housemates each also contacts 25 people a day. Also assume if they become ill, you're 100% likely to get it from them. (These are not necessarily realistic assumptions, so please don't infer anything from these particular numbers!)
This means that if you go out, you're effectively contacting 100 people a day (75 of these by proxy.) If you stay home you're reducing your total number of effective contacts from 100 to 75, so a 25% reduction. This is still an overall reduction in your total exposure.
Whether that reduction will be enough for you for it be worthwhile depends a lot on the specific numbers. These numbers include the overall risk of infection per contact (at present likely low but could increase, also depends a lot on where you live), how many contacts you and your housemates actually have, and the probability of getting it from them if they do get infected (probably a lot less than the 100% assumed here).
My plan would be to not leave my room, except to take out the trash and to go to the bathroom. And I would shift to any early schedule. So I shouldn't have much contact with my housemates, and would be doing my best not to touch the items they touch (and maybe disinfecting doorknobs / bathroom stuff before I touch them, if that's practical).
So the factor that I'm most interested in is the one you assumed was 100%: if one of my housemates contracts the disease, how likely am I to catch it, and how much can I reduce the probability?
I live in a house with four other people, including two that I share a bathroom with.
Does it help me at all to self quarantine, and not leave the house, if my housemates continue to go to work? I would mostly stay in my own room, except that I would need to go to the bathroom and wash dishes.