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.

Answer 1

Number of ways the first 4 databases can be selected = 9C4 = 126
Probability that it is in 2 of the first 4 = 5C2 / 126 = 10/126
Probability that it is in 3 of the first 4 = 5C3 / 126 = 10/126
Probability that it is in 4 of the first 4 = 5C4 / 126 = 5/126

Probability that it is in at least 2 of the first 4 = 10/126 + 10/126 + 5/126 = 25/126