Question

6. The Tauroto region contains 31 different species of IceCream-type small monsters. Each capture of an IceCream-type small monster has an equal chance of being any of the 31 species. If a collector captures five of these small monsters, what is the probability that they have captured two small monsters of the same species?
7. In the same scenario as problem above, what is the lowest number of IceCream-type small monsters that a collector must capture to make capturing two of the same species more likely than not?

Answer 1

Probability that in the 5 captured monsters, two monsters of the same species are captured is computed here as:

= 1 - Probability that all 5 are of different species

Therefore 0.2878 is the required probability here.

Let the lowest number of IceCream-type small monsters that a collector must capture to make capturing two of the same species most likely than not be N

Then, we have here:

Solving this by hit and trial,

For N = 6,

For N = 7,

Therefore N = 7 is the required number here.