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In a batch of 20 television picture tubes, 5 are known to be defective. What is the probability that a random sample of 5 (without replacement) will result in each of the following? There are 3 questions following the table below.
The relevant equation for the Hypergeometric Distribution: P = kCx * (N-k)C(n-x) NCnk is the number of "defects" in the populationx is the number of "defects" in the sampleN is the size of the populationn is the number sampledP is the probability of obtaining exactly x "defects"kCx is the number of combinations of k things taken x at a time or k! (k-x)! x!
The table below is constructed using Excel to compute probabilities, P, for different numbers of x "defects" given the conditions above.
k x N n N-k n-x kCx (N-k)C(n-x) NCn P5 0 20 5 15 5 1 3003 15504 0.193695 1 20 5 15 4 5 1365 15504 0.440215 2 20 5 15 3 10 455 15504 0.293475 3 20 5 15 2 10 105 15504 0.067725 4 20 5 15 1 5 15 15504 0.004845 5 20 5 15 0 1 1 15504 0.00006
What is the probability that a random sample of 5 (without replacement) will result in each of the following?
• Exactly 1 defective• No defective• Two or fewer defectives
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