EXAMPLE 3 If the probability is 0.40 that a child exposed to a certain contagiou
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EXAMPLE 3 If the probability is 0.40 that a child exposed to a certain contagious disease will catch it, what is the probability that the tenth child exposed to the disease will be the third to catch it? EXAMPLE 5 If the probability is 0.75 that an applicant for a driver's license will pass the road test on any given try, what is the probability that an applicant will finally pass the test on the fourth try? EXAMPLE 6 As part of an air-pollution survey, an inspector decides to examine the exhaust of 6 of a company's 24 trucks. If 4 of the company's trucks emit excessive amounts of pollutants, what is the probability that none of them will be included in the inspec- tor's sample?Explanation / Answer
Binomial distribution: P(X) = nCx px qn-x
3) P(10th child exposed is the third one to catch it) = P(2 of the first 9 caught the disease) x P(10th child caught the disease)
= 9C2 x 0.42 x (1-0.4)7 x 0.4
= 0.1612 x 0.4
= 0.0645
5) P(passing on 4th try) = P(failing on first three tries) x P(passing)
= 0.253 x 0.75
= 0.0117
6) nCr = n!/(r! x (n-r)!)
P(none of the 4 trucks of the 24 will be included in the inspectors sample) = P(selecting 6 from the 18 trucks that doesnt emit excessive amounts of pollutants)
= 18C6 / 24C6
= 0.1379
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