8 of the 40 newly built cars are selected at random to be checked for steering defects. Suppose 10 of the cars have such defects. What is the probability that all 8 of the selected cars have steering defect?

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8 of the 40 newly built cars are selected at random to be checked for steering defects. Suppose 10 of the cars have such defects. What is the probability that all 8 of the selected cars have steering defect?

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Answer 1 · 2016-02-15T01:18:53

Since you are sampling without replacement and the sample size is large with respect to the population $(\frac{8}{40} = 20 %)$ $(8/40=20%)$ , use the following "counting" method ...

Explanation:

Number of ways to select 8 of the 10 defects :

$= \frac{10!}{8! \times 2!} = 45$ $=(10!)/(8!xx2!)=45$ ways

In general , number of ways to select 8 from a population of 40:

$= \frac{40!}{8! \times 32!} = 76, 904, 685$ $=(40!)/(8!xx32!)=76,904,685$ ways

Finally, calculate your probability ...

$P (all 8 have defects) = \frac{45}{76, 904, 685} \approx 0.000000585$ $P("all 8 have defects")=45/(76,904,685)~~0.000000585$

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8 of the 40 newly built cars are selected at random to be checked for steering defects. Suppose 10 of the cars have such defects. What is the probability that all 8 of the selected cars have steering defect?

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Explanation:

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