10. A police force has two young canines in training (Jimmy and Sally) that they
ID: 3051951 • Letter: 1
Question
10. A police force has two young canines in training (Jimmy and Sally) that they plan to use to check packages for illegal substances. The canines check the packages independently If an illegal substance is present, Jimmy accurately detects the presence of the substance with probability 0.65 and Sally accurately detects the presence of the substance with probability 0.75. a) (3 points) Find the probability that the substance will be detected by at least one of the canines if it is present in a package. (Round your answer to four decimal places.) b) (3 points) Find the probability that the substance will not be detected by either of the canines if it is present in a package. (Round your answer to four decimal places.) piraExplanation / Answer
Solution:
probability that jimmy ditects = 0.65
probability that jimmy does not detect = 1 - 0.65 = 0.35
probability that sally ditects = 0.75
probability that sally does not detect = 1 - 0.75 = 0.25
( a )
probability that atleast one of them detects when canines are present = (0.65)(0.25)+(0.75)(0.35)+(0.65)(0.75)
= 0.1625+0.2625+0.4875
= 0.9125
( b )
probability that none of them detects when canines are present = (0.35)(0.25)
= 0.0875
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