Probabilty Homework Issues

[yackel.richard]

A civil engineering construction firm‘s records show that the probability is 0.2 that one of its new bridges will require repair within a year.

a) What is the probability that the tenth bridge it builds will be the second one to require repair within a year?

b) What is the probability that the sixth bridge it builds will be the first one to require repair?

 

[soroban]

Hello, yackel.richard!

I'll try to explain the first one . . .

A civil engineering construction firm‘s records show that the probability is 0.2
that one of its new bridges will require repair within a year.

a) What is the probability that the tenth bridge it builds will be the second one
to require repair within a year?

\(\displaystyle \text{Of the first nine bridges, exactly one needed repair.}\)
. . \(\displaystyle \text{This probability is: }\:{9\choose1}(0.2)(0.8)^8\)

\(\displaystyle \text{Then the tenth bridge needed repair.}\;\text{ This probability is: }\:0.2\)

\(\displaystyle \text{Answer: }\;9(0.2)(0.8)^8 \times 0.2 \;=\;0.060397978\)

b) What is the probability that the sixth bridge it builds will be the first one to require repair?

\(\displaystyle \text{The first five bridges did not need repair: }\0.8)^5\)

\(\displaystyle \text{Then the sixth bridge needed repair: }\:0.2\)

\(\displaystyle \text{Answer: }\;(0.8)^5(0.2) \;=\;0.065536\)

 

[Deleted member 4993]

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A civil engineering construction firm‘s records show that the probability is 0.2
that one of its new bridges will require repair within a year.

a) What is the probability that the tenth bridge it builds will be the second one
to require repair within a year?
b) What is the probability that the sixth bridge it builds will be the first one to require repair?

Duplicate post:

http://answers.yahoo.com/question/index ... 608AA6xyM3