In a shipment of 20 phones, 4 are damaged, and 16 non defective. If one tests a sample of 6 at random. The number of damaged phone in the sample is random variable X. What is the probability that at least one is damaged?
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Given:
Total numbers of phone = 20
Damaged = 4
Non-defective = 16
To find:
What is the probability that at least one is damaged?
Solution:
When all the samples chosen are non-defective.
P = ¹⁶C₆ / ²⁰C₆ = (16! / 6! × 10!) / (20! / 6! × 14!) = 8008 / 38760
When least one is damaged
P' = 1 - P = 1 - 8008 / 38760 = 30752 / 38760 = 0.793395253 ≈ 0.79
So, probability that at least one is damaged is 0.79
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