Question

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

I'm kind of stuck setting up the problem.

Answer 1

at least two out of four means 2 or 3 or 4 out of 4 so we can compute these probabilities and add
or else compute the probability it is found in none or one of the first four and then subtract from one. your choice

Answer 2

probability it is in all four is
\[\frac{5}{9}\times \frac{4}{8}\times \frac{3}{7}\times \frac{2}{6}\] is that more or less clear?

Answer 3

first and second and third and fourth, multiply the probabilities together

Answer 4

or perhaps you might have been taught as follows
all 4 means
\[\frac{\dbinom{5}{4}}{\dbinom{9}{4}}\] you will get the same number

Answer 5

then three out of four will be
\[\frac{\dbinom{5}{3}\times \dbinom{4}{1}}{\dbinom{9}{4}}\]

Answer 6

and finally 2 out of 4 will be
\[\frac{\dbinom{5}{2}\times \dbinom{4}{2}}{\dbinom{9}{4}}\]

Answer 7

do you know how to compute these numbers?

Answer 8

I think I was over complicating the problem. I thought about computing the probability of at least 2 of the first 4 searches. Then I thought I needed to do more work since only 5 out of 9 databases contain the keyword. Now that you explained it, it makes sense. Thanks!

Answer 9

yw but you do have to do a bit of computation

Answer 10

Yes, I know how to perform the computations.

Answer 11

ok good. have fun!

Answer 12

Thanks, have a nice day!