5.3.41-T EQuestion Help The probability of a randomly selected adult in one coun

Question

5.3.41-T EQuestion Help The probability of a randomly selected adult in one country being infected with a certain virus is 0.006. In tests for the virus, blood samples from 12 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus. The probability that the combined sample will test positive is Round to three decimal places as needed.)

Explanation / Answer

5.3.41-T

Pr(Being affected with virus) = 0.006

Pr(at least one will affect out of 12) = 1 - Pr(noone will be affected from virus)

= 1 - 12C0 *(0.006)0 (0.994)12

= 1 - 0.9303

= 0.0697

No, it is not unlikely for the sample to test virus.

5.3.43

Pr(Defective aspirin) p = 0.04

Sample size n = 10

Pr(Whole shipment will be accepted) = Pr(Only one or none defects)

= Pr( X = 0) + Pr( X = 1)

= 10C0 *(0.04)0 (0.94)10  + 10C1 *(0.04)1(0.94)9

= 0.6648 + 0.277

= 0942

5.3.44-T

Pr(Defective aspirin) p = 0.04

Sample size n = 14

Pr(Whole shipment will be accepted) = Pr(at most two defective tablets are there)

= [Pr( X = 0) + Pr( X = 1) + Pr( X =2)]

= 14C0 *(0.04)0 (0.94)14 +  14C1 *(0.04)1(0.94)13+14C2 *(0.04)2(0.94)12

= 0.5647 + 0.3294 + 0.0892

= 0.983

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