Question

16) 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? a)o.2564 b)0.0009 c)0.9256 d) 0.0645 e) None of the above )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 inspector's sample? 17 a)o.5554 b) 0.2880 c)0.9589 d) 0.0623 e) None of the above

Answer 1

16) d) is correct.

Let X be the number of unexposed childs to the disease before getting 3 exposed childs to the disease.

The probability of a child exposed to a certain disease = p =0.4

Therefore X faollows negative binomial distribution with number of success r=3 and probability of success p=0.4

We have to compute probability that tenth child exposed to the disease will be the third to catch it (7 failuars)

ie. $P(X=7)=\binom{7+3-1}{7}0.4^3 (1-0.4)^7$

P(X=7)=0.0645

17) b) is correct.

X- Number of truck will be included in the inspector's sample.

X has hypergeometric distribution with parametes sample size n=6, number of trucks emit pollutant M=4 out of total N=24 trucks.

We have to compute probability that none of them will be included in the inspectors sample

i.e. $P(X=0)=\frac{\binom{24}{0} \binom{24-4}{6-0} }{\binom{24}{6}}$

P(X=0)=0.2880