SOLUTION: Eight of the 40 newly built cars are selected at random to be checked for steering defects. Suppose 10 0f the cars have such defects. Find the probability that all 8 of the selecte

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Question 1018218: Eight of the 40 newly built cars are selected at random to be checked for steering defects. Suppose 10 0f the cars have such defects. Find the probability that all 8 of the selected cars have steering defect.
Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!

Question:
Eight of the 40 newly built cars are selected at random to be checked for steering defects. Suppose 10 0f the cars have such defects. Find the probability that all 8 of the selected cars have steering defect.

Solution:
This is a problem that can be solved using the hypergeometric distribution.
Let
A=number of defective cars in the population
B=number of non-defective cars in the population
a=number of defective cars in the sample
b=number of non-defective cars in the sample.

Then
Probability of picking a defective out of a sample size (a+b) is
P(a;a+b)
=P(8;8)
=C(A,a)*C(B,b)/C(A+B,a+b)
=C(10,8)*C(30,0)/C(40,8)
=1%2F1708993

This can also obtained by reasoning the long way:
Fist defective: 10/40,
second defective: 9/39
...
eighth defective: 3/33
Multiplying together gives
P(8,8)=10*9*8.../(40*39...33)=1%2F1708993