Can double masking increase efficacy by 126% against particles?

[jonathan cooper]

Homework Statement

If there are two masks, which have the ability to prevent passage of 1 micron sized particles, with 34% and 92% effectiveness respectively, then would what % of particles would pass through. Would the two masks together be 126% effective?

Relevant Equations

Would the two masks together be 126% effective?

Would the two masks together be 126% effective?

 

[sysprog]

It's required that you make an attempt before anyone is allowed to be of assistance to you on a homework problem $-$ please check the 'terms' link in the page footer.

 

[WWGD]

Maybe also think of the meaning of '126%' effective.

 

[benorin]

If something always works it’s 100% effective.

 

[WWGD]

Homework Statement:: If there are two masks, which have the ability to prevent passage of 1 micron sized particles, with 34% and 92% effectiveness respectively, then would what % of particles would pass through. Would the two masks together be 126% effective?
Relevant Equations:: Would the two masks together be 126% effective?

Would the two masks together be 126% effective?

Are you told whether the two filters are independent? Seems reasonable they would be. Now think of the two outcomes passing through/not passing through.
Edit: This is taken from an idea by @sysprog

 

[jim mcnamara]

Suppose you had 100 balls. Take way 34% of them gives you what remains after the first filter Hint: 34% of 100 is 34 ...so you are left with 66 balls. Now remove 92% of the remaining 66 balls. Just round up since you cannot take part of a ball. For your problem: You can use decimals for your actual answer, e.g., like the remainder of particles is xx.y%.

Seems the OP is not around, so a little extra boost is probably okay. Normally we do want folks to figure out problems on their own - they get a lot more out of it that way.

 

[sysprog]

The 34% filter passes 66%, and the 92% filter passes 8%, and 8% of 66% (or 66% of 8% $-$ the order of the filters doesn't matter) equals 5.28%, so of 10,000 particles, the filters should stop 9,472, and pass 528.

 

[jbriggs444]

The 34% filter passes 66%, and the 92% filter passes 8%, and 8% of 66% (or 66% of 8% $-$ the order of the filters doesn't matter) equals 5.28%, so of 10,000 particles, the filters should stop 9,472, and pass 528.

That is a plausible mathematical model of filter behavior.

But there is no assurance that it matches the real world filter behavior. For instance, it could be the case that the filtering effectiveness is not independent. Particles that pass the first filter might be preferentially able to pass the second. Or particles that pass the first might pick up contaminants on the way and be extra-effectively stopped by the second.

One should strive to explicitly state the assumptions that go into a result.

 

[sysprog]

Particles that pass the first filter might be preferentially able to pass the second. Or particles that pass the first might pick up contaminants on the way and be extra-effectively stopped by the second.

I agree with this $-$ as a practical matter, I would put the finer filter after the coarser one.