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An Internet search engine looks for a keyword in 9 databases, searching them in random order. Only 5 of these databases contain the given keyword. What is the probability that it will be found in at least 2 of the first 4 searched databases?

What I tried is: Let X: the event that the keyword is to be found in at least 2 databases, and Y: the event that we search the first 4 databases, then we need to find a conditional probability $P(X\geq 2 | Y)=P(X= 2,3,\text{ or }4 | Y)=\frac{P(\{X\geq 2\} \cap Y)}{P(Y)}$ but then I don't know how to continue?

Any help...

3 Answers 3