SARS Suspects

SARS Probability

A group of tourists at airport are screened for temperature twice thru Gate A (accuracy a=98%), then Gate B (accuracy b=97%).

Finding: Gate A detected 32 (=A) tourists, but Gate B only 23 (=B), of which 16(=C) are common.

Q: How many suspects missed out (suspects missed) ?

Solution:

Let T = Total tourists

a, b the probability of successful detection at Gate A, B, resp.

A=aT , B=bT

AB=(aT)(bT)=(abT).T

C= a.bT (because Gates A, B independent screening)

AB=C.T

T=AB/C

Suspects-detected= A + B - C (exclude duplicate common)

Suspects-missed M = T- (A+B-C) = AB/C -(A+B-C) =(AB-AC-BC+C.C)/C= (A-C)(B-C)/C


M =(A-C)(B-C)/C

Note: M independent of a, b !!

Suspects-missed M = (32-16)(23-16)/16 = 16x7/16 = 7 [QED]