Travel and Transportation. A super-commuter is a person who commutes to work fro

Question

Travel and Transportation. A super-commuter is a person who commutes to work from one large metro area to another by car, rail, bus, or even air. Super-commuters are not necessarily elite business travelers, but rather middle-income individuals who are willing to commute long distances in order to secure affordable housing or better schools. According to a recent study, 13% of workers in Houston are super-commuters, 8.6% in Phoenix, and 7.5% in Atlanta.

Suppose three workers are selected at random, one from each city.

(a) What is the probability (± ± 0.000001) that all three are super-commuters?

P(all three are super - commuters) P(all three are super - commuters) =

(b) What is the probability (± ± 0.0001) that none of the three are super-commuters?

P(0 of three are super - commuters) P(0 of three are super - commuters) =

(c) What is the probability (± ± 0.0001) that only the worker from Houston is a super-commuter?

P(only the worker from Houston is a super - commuter) P(only the worker from Houston is a super - commuter) =

(d) What is the probability (±0.0001) that exactly two of the workers are super-commuters?

P(2 of 3 are super - commuters) P(2 of 3 are super - commuters) =

Explanation / Answer

a) P(all three are super - commuters) P(all three are super - commuters) =0.13*0.086*0.075=0.0008

b)

P(0 of three are super - commuters) P(0 of three are super - commuters) =(1-0.13)*(1-0.086)*(1-0.075)=0.7355

c)

P(only the worker from Houston is a super - commuter) P(only the worker from Houston is a super - commuter) =

=0.13*(1-0.086)*(1-0.075)=0.1099

d)

probability (±0.0001) that exactly two of the workers are super-commuters=P(from Houstom and Phoenix are+ from Houston and Atlanta are +From Atlanta and Phoenix are super commuters)

=0.13*0.086*(1-0.075)+0.13*(1-0.086)*0.075+(1-0.13)*0.086*0.075=0.0249

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