I saw something on the news about the coronavirus. Wearing a mask is 70% effective in blocking the droplets that can cause you to be sick. If you and the other person is wearing a mask, you only have a 9% of getting infected. (Those numbers are what I heard, but I'm not certain of the context because I wasn't totally paying attention, but we'll run with it.) Those numbers seem right, mathematically. You have person A and person B. You want either one's mask to block the germs.
Probablility of A or B is happening is
Pr(A) + Pr(B) - Pr(A) x Pr(B).= 0.7 + 0.7 - 0.7 x 0.7 = 1.4 - 0.49 = 0.91.
Looking at it another way, start directly with the probability germs get through.
C and D are now the events that germs aren't blocked.
Pr(C) x Pr(D) = 0.3 x 0.3 = 0.09
Again a 9% chance.
Pr(B) - Pr(A) x Pr(B).= 0.3 + 0. - 0.7 x 0.7 = 1.4 - 0.49 = 0.91.
