| You're right on your first estimation: P(getting infected per touch) = 1/10000 = .0001 P(not getting infected per touch) = 1 - P(getting infected per touch) = .9999 P(not getting infected after 100 touches) = P(not getting infected per touch) ^ 100 = .9999 ^ 100 =~ .99 P(getting infected after 100 touches) = 1 - P(not getting infected after 100 touches) =~ .01 = 1% Or, in other words: 1 - ((1 - .0001) ^ 100) =~ .01 = 1% chance of infection By the same logic, your second estimation is a bit off: 1/5000 = .0002 1 - ((1 - .0002) ^ 100) =~ .02 = 2% chance of infection That's a far cry off 40%. To think about it another way, if the chance to get infected per touch is 1/10, and you touch a surface 20 times, is your chance of infection 200%? No, that doesn't make sense. It's 1 - ((1 - 1/10) ^ 20) =~ 87.8%. That's the problem with statistics -- "everyone can do the math", but it's pretty easy to mix it up and reach the wrong conclusions and spread misinformation. |