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Previous Year Question (PYQs)



From a lot containing $10$ defective and $90$ non-defective bulbs, $8$ bulbs are selected one by one with replacement. Then the probability of getting at least $7$ defective bulbs is:





Solution

$P(\text{defective})=\frac{10}{100}=\frac{1}{10}$ Required probability $=P(7\text{ defective})+P(8\text{ defective})$ $=\binom{8}{7}\left(\frac{1}{10}\right)^7\left(\frac{9}{10}\right)+\left(\frac{1}{10}\right)^8$ $=\frac{8\cdot9}{10^8}+\frac{1}{10^8}$ $=\frac{72+1}{10^8}=\frac{73}{10^8}$


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