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General probability question

  1. Feb 16, 2015 #1
    Shortly after being put into service, some buses manufactured by a certain company have developed cracks on the underside of the main frame. Suppose a particular city has 25 of these buses, and cracks have actually appeared in 8 of them.

    (i) How many ways are there to select a sample of 5 buses from the 25 for a thorough inspection?
    (ii) How many of these samples of 5 buses contain exactly 4 with visible cracks?
    (iii) If a sample of 5 buses is chosen at random, what is the probability that exactly 4 of the 5 will have visible cracks (to 3 dp)?
    (iv) If buses are selected as in part (iii), what is the probability that at least 4 of those selected will have visible cracks (to 3 dp)?





    answers:
    (i) 25 buses, 5 choices so: 25C5 = 53130
    (ii) 5 buses, 8 broken so: (8C4)(17C1) = 1190
    (iii) 53130/1190
    (iv)
    at least 4, so:

    {(8C4)(17C1) + (8C5)(17C0)} / 25C5


    can you check my answers? thanks.
     
  2. jcsd
  3. Feb 16, 2015 #2

    PeroK

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    Gold Member

    Apart from putting the answer to (iii) upside down, your answers are correct.

    You might get a better response in the "homework" section.
     
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