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.

Hence,

There are total 9 databases.

Only 5 of these databases contain the given keyword.

we have to find the  probability that it will be found in at least 2 of the first 4 searched databases.

So, we will use the binomial to find this probability.

We know that the probability of r successes out of the n outcomes is calculated as:

Where p denote the probability of success.

and

p=5/9 ( since out of the 9 databases 5 contain the given keyword)

1-p=4/9.

so, we have to find:

Here n=4

Also,

Hence, the probability is calculated by adding equation (1),(2) and (3).

Hence,

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step-by-step explanation: